I have noticed that the tempo of the MiniBrute arpeggiator only snaps to the project tempo when the project is actively playing, and when it stops playing the MB tempo goes back to hardware setting/clock. Each time it's changed by the project playback starting and stopping, there's a delay/lag that affects the MiniBrute playing.
I think the best work-around is inserting a 2 bar blank in the start of the project, so it has time to adjust the tempo before having to play something. And just so we're clear, you will have to play the blank bit to actually give it the time to change the clock source.
Hope this is something that will be adressed in future updates.
Alternatively you need to either find something to send it a steady clock, or stop the DAW sending clock, and rely on tap-tempo.