Tab Pro subscription is always attached to a certain Ultimate Guitar account so it all makes sense, doesn't it?
Just make sure that you've downloaded the correct app.
Tab Pro for Android: https://play.google.com/store/apps/details?id=com.ultimateguitar.tabprofree
Tab Pro for iOS:
It is also possible that you have chosen a local subscription plan that gives access only to the web version of Tab Pro. You can see what kind of plan you are subscribed to by going to your account => Subscription => manage your subscription.