Screen recorded videos have audio sync delays in Premiere Pro
Okay so I found the issue and a quick fix for the .mp4 audio sync issues. First you need to backup your video files, then change the file extension from .mp4 to .mov. This will allow you to reimport with accurate playback speed.

If Premiere gives you a weird error upon importing, make sure you have QuickTime installed from Apple's website, restart, and then try again. 

The fix came from this video, and I hope it helps someone else!