While I have two active subscriptions myself, this seems to also be happening to my girlfriend who is only using one WoW account.
Whenever she logs in there, it kicks her off her Battle.net app.
On the other hand my brother, also using two accounts, is doing just fine.
While it feels like there is some bias to those of us that are using two WoW accounts, it does not seem to be the one thing determining whether or not you get this buggy behaviour.