I captured screen audio and visual using QuickTime Player version 10.4. Needed to trim a few seconds from the beginning of the clip, and saved it as a .mov file. Plays back correctly in that format. When I import the file into Media Encoder CC version 2017.1.2 and try to encode it to an mp4 file using the H.264 format, the audio playback is correct, but the video playback is too slow (almost half speed, perhaps?). I don't have this issue when I try to encode a QuickTime .mov file that has not been trimmed from the beginning.
I am sorry that you are facing this trouble.
Screen capturing apps often use Variable Frame Rate recording, which is not ideal for use in Media Encoder & Premiere Pro.
I have seen similar issues before and I would suggest you to convert the variable rate footage to a constant frame rate using the free HandBrake software before importing & transcoding in Adobe Media Encoder.
Let me know if that helps.