If your T has given you her out-of-hours contact info, trust that she means that you can contact her and she'll respond as soon as she's able.

My T has given me his cell and home numbers and encourages me to use them. I rarely do, but I know he means it. We've spent a lot of time talking about it, with me not understanding why he wants me to call him (he doesn't do text or email) and him steadfastly maintaining that he doesn't just care about me in the office. I fussed about not knowing how to identify when I "need" to talk to him versus just wanting to. He told me to forget that - if I think it will make me feel better, I should call. He'll manage the boundaries, so I needn't worry about it.

I called him a couple of days ago and he sounded almost giddy that I'd called. He's a keeper.