Hmmm. Yes, adding a tag to a PM when creating a message does not seem to be appearing on mobile. 
However, if you create a message, and then either edit the title or OP then the tag input box appears.
I’ll slide this over to Contribute > Bug. 
- Add a group (staff) to
pm tags allowed for groups - Create a PM using a mobile
- No tagging option available in composer
- Send a PM
- Edit the PM title or OP and the tagging option appears
I would expect the tagging option to appear in both create and edit