That sounds like unwanted behavior. I think there are a few bugs with local mode at the moment. If you can show and explain it in a simple file, report it.
(if it hasn’t been reported already)
I haven’t had time to report the local mode weirdness I have found.
(if you have more than 1 armature selected but then jump into local mode and animate – you actually animate the invisible control outside of local mode as well as the control in local mode.)
I discovered this on some client work – which I can’t send in to the devs to look at. I need time to recreate it in a fresh simple file.