Yes, i user a Xiaomi phone :(Redmi Note 3).
Interesting, because the other apps (Messenger, Whatsapp) not do this.. Seems to be the "popular" apps the Miui recognise and enable the background running, not need to enable it in battery settings. I use a different email app before (Newton mail) and it working well. I think it happend the same, the miui recognise the newton mail, and "see" this is a email app and not touch it.
I think, somehow need to do the same with Aqua Mail.