Well, to know what her sigh meant you'll have to ask her on Monday and see what she says, or if she even remembers doing it (my guess is she won't). Of course she'll turn it around and will want to know what it meant to you.
What is a sigh in a converasation like that, to you? What did that mean to you? If it has negative connotations to you, why do you think you are ready to perceive a sigh in that way? What fear is evoked by hearing T sigh when on the phone with her? ....So much to think about!
I think about sighs and they many things, depending on the circumstances and conversation. It might me exasperation, or feeling bothered. It might be a loving, concerned sigh. It might be a 'take a breath' sigh where the talker needs a break to do some more thinking and cosidering before replying, a kind of "let me think a moment" sigh.
You're right, she is being herself. And you're being yourself, learning about your reactions / perceptions. I admire how you are able to process things like this that can be so automatic they can just happen without much awareness on our part.
I am way too reactive to things like that, looks, tone, posture, gestures. Sometimes my T squints a bit as she's thinking and can get this really different look on her face; I used to think it was anger but have come to realize it's just her thinking and processing things herself.