It would appear to be a bug and it would appear to be related to the parenting of the emitting vertices to the corners of your mesh - with the location of the particle taking on the un-transformed location but obeying the rotation (this can be seen from the pattern of the particles after the rotation has stopped but the location is still being keyframed).
You should cut it down to a minimal example (eg, 1 vertex instead of 8) so that the situation can be easily replicated by the developers (it's better if the situation can be replicated from a default cube new Blend file rather than relying on them opening your Blend - this way it rules out anything specific in your file), listing the exact steps taken to setup the example (eg, "From the default cube, create another mesh (eg, a cube) and, in edit mode,'Merge' the vertices to a point so that it consists of a single vertex and move that vertex to the vertex of the cube. Parent the vertex to the cube and keyframe the location and rotation of the cube so as to move it over 100 frames by 5 units away from the world origin while randomly rotating. Add a particle system to the single vertex object with default settings set to emit from 'Vertices' and set to 5000 particles. Run the animation and a small fraction of the particles are being emitted at seeming random locations instead of the vertex." (assuming something like that can replicate the problem). Include screenshots and include your .blend.
The bug can be raised within Blender by selecting the "Help/Report a bug" option in the menus.
For info, I've replicated this on a Windows 10 system with Blender 2.91.2 by simply Appending all objects from your file into a default startup blend file.
As mentioned, it appears to be related to the parenting of the vertex to the animated cube with the particles not always picking up the 'final' position (possible race condition).