I read somewhere that secure attachment is related to feeling held in the other's mind and heart. My T has mentioned on several occasions when she's thought of me outside of sessions, and I think it's really helped me to feel more securely attached with her (among other things).

I wonder if the "weird" feeling is related to subconsciously thinking of your T as only existing in the room. Kind of like how young students think their teachers live at school, to think of them outside that context feels discordant.

Or maybe it's also hard for you to hold your T in your mind and heart, and it's therefore difficult to imagine he would do the same.