I will try and explain this as simply as I can, it would be easier if I had you and the gun in front of me at an armorer course where I could visually show you, so if you don't understand what I am putting into text, the please ask questions and I will try and explain it.
Something we teach in armorer courses is: If it is a one time thing, then it may be a freak of nature, which means clear it out a drive on. If it is happening every few rounds, being a continual problem, then you have to figure out the cause in order to possibly fix it.
First thing is to always start with a thorough cleaning, making sure all gummy gooey stuff & debris is removed from all nooks and crannies, and then apply lubrication on all areas of friction, and use a rust inhibiting lubricant on all steel parts that may rust. When cleaning, look for any signs of damage, cracks, worn out parts, debris that doesn't belong (sun flower seeds, dog hair, lint, grass seeds, bubble gum, cigarette ash and butts, etc, it is amazing what you can find in patrol car shoulder weapons), and also look for any parts that may be missing or put in upside down or backwards.
So if you are getting two live rounds coming out of the magazine tube, then it is possibly either a freak of nature one time thing, you possibly didn't push the last round into the magazine tube deep enough to be in front of the shell latch tips (operator error), or you have an issue with the action bar & shell latch interaction.
If you have concluded it's not a freak of nature thing as it is happening consistently, and it's not operator error, then if you are having two live rounds feed out of the magazine tube on an 870, then it could be related to a few possible mechanical issues (but not limited to).
The 870 has two shell latches, as if you are behind the gun shooting it, you will have on the right and left sides. The shell latches are what hold the live shotgun shells in the magazine tube. When you push a shell into the magazine tube by pushing up on the carrier with the front of the shell, then push the shell forward into the magazine tube, you should push the shell into the magazine tube deep enough past the audible & mechanical click. This mechanical and audible click is the front tip of the shell latches, which hold the shell into the magazine tube.
The shell latches are controlled by the action bar assembly (forend). The action bars are what the forend furniture is attached to. The action bar assembly is responsible for how the gun cycles in 7 out of the 8 cycles of fire (sometimes referred to as cycles of operation). The action bars are what the bolt and slide plate sit on top of. You cycle the action bar assembly rearward, it will allow to extract & eject an empty or live shell from the chamber, and recock the hammer. You cycle the action bar assembly forward to feed & chamber a live shell, and lock the action into battery.
The action bar assembly also controls the feeding cycles, there are two feeding cycles in the 870. The first feeding cycle is when you pull rearward on the action bar assembly, as after the empty shell is extracted from the chamber, and the action goes rearward enough to eject the empty shell, as you continue pulling rearward on the action bar assembly you should have a live shell release from the magazine tube. The live shell that is released from the magazine tube should then be sitting on top of the carrier.
The second feeding cycle happens as you push forward on the action bar assembly. After you pull rearward on the action bar assembly, and a live shell is now sitting on the carrier, you will have to push forward on the action bar assembly to cycle the action forward. As you push forward on the action bar assembly, the front of the carrier should push upward (acting as a feed ramp in a sense) so the live shell is fed towards the chamber of the barrel. As you continue a little more forward with action bar assembly so the live shell is fed into the chamber, the carrier should drop back down to where it sits during all other cycles of operation.
The action bar assembly controls the shell latches on both the right and left. The shell latches are slightly staggered on the front end tips, with the left shell latch being more to the rear, and the right shell latch slightly more forward. The shell latches tips are pushed outward as you cycle the action bar assembly (forward and rearward), as the action bar assembly has diagonal cuts on them (referred to as timing cuts).
If you look at the action shell latch tips, when the action is forward and things are locked into battery, the left shell latch will be protruding, and the right shell latch will be recessed. When you cycle the action bar assembly rearward, the right shell latch will protrude, and the left shell latch will recess.
When the action bar assembly is cycled forward, the left shell latch is protruding to hold the live shell in the magazine tube, and the right shell latch is recessed out of the way so all shells in the magazine tube can be pushed rearward by the magazine tube spring & follower.
When you cycle the action bar assembly rearward, the left shell latch will get pushed out of the way, and the right shell latch will then protrude inward into the magazine tube. When the left shell latch is pushed out of the way so it recesses, the live shell will then be released from the magazine tube and onto the carrier. At the same time the right shell latch will protrude into the magazine tube to catch the next live shell coming rearward inside the magazine tube.
The shell latches are supposed to be staked into the 870's receiver. The purpose of the staking is to keep the shell latches in the receiver, so when you remove the trigger group, the shell latches don't fall out. The front trigger housing pin (trigger plate pin) runs through the shell latches as well. If the shell latches fall out when the trigger group is removed, you can simply put the shell latches back in, insert the trigger group, and when the trigger group is pinned into the receiver, the shell latches will function just fine.
If a shell latch is bent, it may not release a shell from the magazine tube, or it could possibly allow multiple rounds to be released as well. If the shell latches are worn or damaged on the on the tip, they need to be replaced.
If the action bars are bent, it could also cause the shell latches to not be pushed to protrude & recess during the cycling of the action.
You also have to make sure the forend is tight, and properly aligned with the action bar assembly. If you were to remove the action bar assembly from the receiver, look down from the top of the forend, where the action bars & action bar tube to into the backside of the forend, you will see where the action bars go into the back of the forend. If there is a gap of spacing between the action bars at the back of the tube, and where it sits inside the back top of the forend, then the gap needs to be spaced evenly. A common mistake is that the forend is either canted where the gaps are not even (often times touching on one side and a large gap on the other side), which can cause the action bars to get twisted as you cycle them rearward into the receiver, which can cause either no rounds or multiple rounds being released from the magazine tube.
Another common issue is that the forend is loose, and needs to be tightened down, as if it's loose then the shooter could possibly cant the forend as they cycle the action rearward into the receiver, which will cause magazine tube feeding issues of no rounds or multiple rounds being released.
Last thing to check is that the forend isn't rubbing on one side of the barrel as it is cycled rearward. The barrel is tapered, and is thicker towards the chamber end as compared to the front end. As the forend is cycled rearward, it shouldn't be touching the barrel, there should be a slight gap of clearance when the action bar assembly goes rearward to eject the empty shell, and the new live round is release from the magazine tube. I have seen some aftermarket forends, to include some of the new Surefire lights & Knoxx (Blackhawk) forends, that were made to thick, so the users had to remove some of the forend material on the inside so it doesn't rub on the barrel as the forend is cycled rearward.
So after reading above (It wasn't quite "War & Peace" or the "Iliad", but close), a brief troubleshooting action to be taken is:
If the action bars are bent or damaged, replace them
If the forend is loose or misaligned with the action bar assembly tube, properly align them and use a good forend wrench to get them properly tightened.
If the forend is rubbing due to it being over molded, then either drop it back into the manufacturers hands and test their customer service, or figure out where to sand excess material away and do it.
If the shell latches are damaged, the replace them, and properly stake them so they don't come loose.
If you cannot figure it out, then get it to someone that has more knowledge than you and can give it a good look over, we are always happy to look at them (We encourage problematic guns to be brought to armorer courses, as this is a leaning opportunity, and most times we can fix them in class).
Greg Sullivan "Sully"