Indeed, when these issues you've described arise in an AR, it's most often attributed to the disconnector/disconnector spring. What is happening is the disconnector was not holding the hammer to the rear, allowing the trigger to reset. Instead, you're experiencing hammer follow - as the bolt and carrier would travel forward into the locked position, the hammer would fall forward, thus inducing the malfunctions you saw.
You can test at home. Empty gun, no mags etc.
1. Put the rifle on safe
3. Yank the charging handle back as though you're loading it with some vigour.
4. Pull the trigger - the safety should work and nothing should happen.
5. Take the rifle off of safe. Repeat step 3.
6. Dry fire the rifle AND keep the trigger depressed.
7. With the trigger still depressed, cycle the bolt and let it slam forward.
8. Let go of the trigger - do you feel any reset and/or can you pull the trigger a second time - this is simulating what would be a 2nd round loaded into the chamber.
9. If the trigger has not reset or you're unsure, remove the rear takedown pin and hinge the upper receiver downwards - you should be able to visually inspect that the hammer is in the fired position.
10. If the hammer is in the fired position, and not due to you pulling the trigger to simulate the second round, then you've still got your problems.
It's best to confirm at the range as well of course, but I would go through the steps outlined above 15-20 times in a row. That should give you a pretty decent indication of whether or not your problems are persisting.
As also said above... if its a brand new complete trigger mechanism, return it for a new one. At least you know you have a new unit, and its less screwing around on your end.
I think I’ve found the problem,
