Hey I don't know if you've found an answer to your problem from someone else yet, but I have had the same problem before, and I've finally found a fix that I'd like to share. I downloaded a video converter called Handbrake. (Mod 2021 update note: You can also use Shutter Encoder, which has more features and codecs than Handbrake).
In Handbrake I imported the video I wanted converted and changed an option from "variable framerate" to "constant framerate". After my webcam footage was converted into "constant framerate", I imported the new webcam footage into Adobe Premiere and everything was in sync at last!
I hope this helps anyone who has had the same problem.
For my problem, it was my webcam's visual that was getting out of sync of my webcam's audio on top of my gameplay footage. I found out that recording devices can record in "variable framerate" or "constant framerate". If a vid is getting out of sync with itself while in Adobe Premiere but not out of sync when you watch it outside of Adobe Premiere, it is because it was recorded in "variable framerate". What variable framerate means is that it cycles/changes the frames at different frame speeds throughout the video, making the video a different length while in Adobe Premiere.
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