Hi Zeno,
well, I played with it since I tried your MIDI Chords ReaBay file.
Yes, it is definitely very nasty bug in Project Bay
It does work OK from Media Explorer (.mid exported file) and also by copying and pasting the in-project item (when the original items timebase is set to "Beats (auto stretch at tempo changes)", but not when reinserting (in-project MIDI item) from the Project Bay - definitely not expected behavior!
Devs, please, take a look at it and fix it. Thanks.
EDIT: The item does not have to have more than one take to reproduce. One is enough
ADDITIONAL INFO: When *.MID file is referenced in Project Bay, then inserting from "Media Source" tab is OK, but inserting from "Media Item" tab is WRONG.