If you're phone is actively logged in (i.e. your phone is unlocked and the app is in the foreground), then you should receive in-app notifications for messages. If not, you should receive push notifications after you log out of your desktop client.
If that's not the case, you may have a stale session preventing you from going fully offline. You can view your current chat sesions at https://hipchat.com/account/sessions. From there, you can log out any unwanted sessions.
If the problem continues after that (or if you have troubles logging out), I'd recommend contacting our support team directly by going to https://support.atlassian.com/contact/
...have mention name FirstnameLastname. Fe.: @MaartenCautreels This certainly helps to know who is being mentioned in a conversation. Imagine your colleague sends the following message...
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