It makes total sense that feelings of unsafety would arise in the course of practicing mindfulness. Mindfulness is all about being in the present (not really in control per se) and my guess is that when you focus on engaging in the physical task (swaying or whatever), you actually cannot engage your brain in worrying about what will happen after you leave session or ruminating about something negative that happened earlier in the day. Mindfulness exercises are all about paying attention to something that is usually linked to the physical body, but the cool thing is that the training also allows you to fully experience emotions or whatever in the present, without your defenses kicking in.

So when you focus on the present, you have to drop your defenses, that you engage in in order to feel safe. Mindfulness will help you feel safe without those defenses, that keep you from your life in the present and keep you anchored in your experiences and all their related biases/distortions in the past. In part, you learn that your defenses really only function to keep you stuck in the way you feel like now, closed off to feeling and behaving differently, and they have nothing to do with BEING safe. Don't confuse feeling safe with actually being safe.

You know that sticky at the top of the forum about cognitive distortions? As an exercise for yourself, run through them and see how many the title of your post seems to fit (I count 5). Consider the possibility of changing how you think about mindfulness and/or consider being open to it in the future.

Just as an aside-- I am teaching mindfulness to my 11 year old. He has no defenses and he is a really in the moment kid (most are, at this age) and mindfulness is only about whether he truly likes it or not. From the very beginning (just a simple body scan exercise), he has loved it. I think of his reaction as a "pure" one, as in what many people would feel like, if they hadn't already had experiences in life that cause them to put up defenses that get in the way of trying to be in the present. To me it's a good lesson about the positivity of mindfulness.