Need help understanding Executor & BH ship mechanics with TM in mirrors

I think it is still due to breach. Both RC have breach and hit their turns at same time. Yours goes first and cleanses its breach and tm starts at 0 again. His immediately goes next, specials your RC which clears its breach but also applies it to your RC and starts tm at 0. Now both RC are starting tm at 0 but yours has breach and his doesn’t. So he gets the tm jump. Can argue it’d almost be better to lose the coin flip and go second in this case.