I put mine on silent and I don't have it on vibrate. I'm pretty sure my therapist turns hers right off and doesn't just put it on silent. She has definitely never looked at her phone when we've been in a session and I wouldn't be impressed if she did.
Well, actually...the only time she has looked at her phone has been something like if we were discussing an email and then she wanted to actually get the email up in front of her, so she'd pick her phone up to do that - but that's for something to do with me, not checking her phone to see if someone else has got in touch with her. And the few times she has done that, she has always apologised in advance for if any messages bip through when she switches her phone back on.
At the end of the session, I generally fiddle with my phone a bit while I get my stuff together and she often switches her phone back on while I'm still in the room. But she checks with me and, again, apologises for any messages that might ping through and make a noise. And I'm fine with that - I guess she quickly checks in between appointments to see if anyone has called/texted/emailed to cancel an appointment or because they're in a crisis.
I wouldn't be fine with hearing messages pinging through or her phone vibrating or ringing or with her checking her phone during my session to see if anyone has contacted her or to read a message that's come through. I don't think that's on at all. It's my time so I expect her attention to be on me. I don't think that's selfish or unreasonable.
I think if she asked in a session if she could leave her phone on because, let's say, a member of her family was having an emergency op and she was waiting on a text from someone to confirm they were out of surgery or something...I think I'd be fine with that and say of course keep it on. But I really can't imagine her ever doing that.
She is often late starting sessions - something I don't generally mind too much. And I usually assume it's because she overruns but, thinking on it now, it might be because she's spotted an SOS from a client in crisis when she checks messages between sessions, so perhaps she calls them then and then ends up starting her next session late. I can easily live with that (I know others may not be able to and that not keeping to time would be a much bigger deal for them than it is for me) but wouldn't feel ok about phone intrusions once we'd actually started a session.
Are you wanting to raise this with her?