AE has never been good with MP3s and let's just leave it at that. Clearly converting to PCM is a minor burden and not too much to ask for anyone.
To further clarify the MP3 format is highly compressed and was designed to provide faster playback over a network. The format takes all of the samples and looks for similar values so it doesn't have to store each bit of data for every sample. Then a table is built that says the sample at this time has the same values as the sample at that time. This table is analyzed by your CPU and the audio is reassembled into a sound that kinda sorta matches the original sound. The higher the data rate the closer the playback is to the original.
When AE looks at an MP3 and starts decoding the information, combining this with other audio that may or may not be compressed, and mixing all of those calculations with the processing of the effects and pixel data, sometimes the decoding of the MP3 gets out of sync simply because there is no built in check in the MP3 format that makes sure the audio stream is rendered in the correct order when clock cycles in the CPU are overloaded by other processes. An MP3 can even skip and stutter when played back on a iPod if you are at the limit on storage and running something else in the foreground.
Any uncompressed or lossless audio format doesn't work that way. Sample 1 contains all of the data for that moment in time, sample 2 also and so on. There is no audio sample that does not contain all of the data so things don't get out of order when the CPU is being stressed because they can't (or at least it is much more difficult).
The same goes for highly compressed video streams in the production pipeline. You always get better results if you convert to a lossless or nearly lossless frame based format.