the intricate juxtaposition of actions and words
I empathize with all involved on this one. My advice would be to remember that to many people, actions are far more important and meaningful than words. She may hear your words of reassurance and simultaneously find a contradiction in your body language. Nonverbal communication is a significant portion of how we perceive people's position on a topic, even when the ideas they verbally express are 180 degrees from what we perceive based on physical actions. I bring this up because just as a conversation can produce a miscommunication, so can nonverbal clues such as turning away, averting your eyes, fidgeting, etc.
I understand the reasons for you to turn away as a means of providing privacy and feeling uncomfortable about your own sense of "intrusion" on their space. I also understand that in the absence of her security about your feelings, the flames of fear and fiction can be fanned by her/their perception of your (subconscious) actions.
I suspect that when they embrace, your feelings are positive and genuine, but your "oh shit! now what?" response to it is to retreat and provide them space. Read as "recoil and retreat." Those actions come form a noble place, but do not convey to your lover that you are comfortable and happy for her. Perhaps some practice of an action that communicates support and respect nonverbally would be helpful. I'd suggest some research on nonverbal communication skills that you could modify and try out.
In any event, I hope you find a good way to navigate this issue and by all means let us know what works and doesn't.