I can't speak for any other admins, but messages are always the best way to reach me.
My list of notifications is usually so deep I'm almost guaranteed to miss something if I'm just checking the list.
For the alert at the page top, Tags are behind PMs in priority. Normally, once I've cleared my new messages, anything behind it (like tags) will show up. However, my phone will just keep displaying the "3 new message(s)" alert forever, so you'd have to hope I noticed the tag notification in the list.
TL;DR I always check my messages.