The cause of the issue seems to be that different softwares use a different audio codecs to decompress audio files causing slight variations in the end result. Uncompressed audio files like wav should not be affected by this so I guess that is another point for using those.
Fix for this is either to use something like Lexicon that can mass shift beatgrids by a set amount of ms during database conversion or use the beatgrid editor on the player to shift it manually before playback.