Speaking from experience in tech sales and as a retail technician for quite some time, I'd argue "logged in" is the better of the two. It wouldn't raise nearly as many questions for the more average humans I had to deal with on a regular basis, and for tech people it gets the point across.
I think the important thing with terms like boot, logged off, logged on, etc. is to make sure you're using the progressive and "while" to indicate if it's post-process or during. But really, I don't think you'll find a better way to say it, those are really about the most pointed way of doing it that occurs to me. Always try to keep it simple - many, many people have a very low boundary for "complicated" in regards to tech, so don't elaborate it more than required.
Another protip, should you be working with such people in future OP, is many people have a piss poor idea of what they need to do to get where they want to go when it comes to technology. In such circumstances, make a habit of asking them what they want to accomplish, rather than the means. You'll find you can fill the details in much better from the conclusion in many cases, over trying to parse together their ideas about how details they don't understand work.