The Farsight Audio Mixer (FAM), and issues with audio latency on Android are the basic causes for this issue.

Ryan Routon, the former Android developer for TPA, confirmed back in October 2013 in this post that TPA uses a custom made in-house audio mixer —lets call it the FarSight Audio Mixer (FAM)— that has some latency issues.

The FAM mixes the game SFX and BGM into a single channel, which is then sent as a stream to the Java side of the app to be submitted in chunks to the OS.

This latency was present well before October 2013 but the reasons causing the issue were not revealed until this date. Advances in device specifications since this date have not resulted in a performance boost to how the FAM operates.

Frustratingly, there is no workaround to this issue, unless the mixer is completely rewritten. Lets just say a complete rewrite of the FAM is highly unlikely because it is definitely a non-trivial task to re-engineer how the FAM operates across all platforms.

Since Android Kit Kat (4.4) was introduced, small improvements to how audio is passed-through have been made. Android Marshmallow (6.x) introduced better audio functionality, which has made marginal improvements regarding gapless playback.