She recently asked everyone to tone down the texts? Sounds like she was getting an awful lot of phone contacts for someone who asked her clients to tone it down.

She has the choice whether she interrupts your session to glance at her phone. She has a choice whether she leaves her phone on or not.

Surely, if there is no pressing emergency, she can check her messages in between clients.
Not professional at all. You are paying for her full attention.
I admit, I don't like this T at all.