Maybe some people notice it more because they are very self aware types, that is, the first thing they do in the morning is check themselves. And what's the first thing they notice? Their Tinnitus. Others may be more outward focused and their brain scans for external noises immediately on awakening - noises from their children, bacon frying, or whatever.
Perhaps "externals" only notice the Tinnitus later when their unconscious is tired of scanning for external noises and there's nothing going on.
Others, of course, may vary. This morning I didn't notice my Tinnitus until I was shaving. I thought, "I didn't notice my Tinnitus when I woke up!", and of course
then I noticed my Tinnitus
So why did I change this morning? Yesterday I made two health appointments for very early, in the morning, and I've had some urgent tasks to get done first thing in the morning the last few days. This isn't usually me. I'm retired & not a morning person. It's usually a few hours before I motivate myself to do the housework, shopping, etc.!
So the past few days I've had a much more external focus for "first thing in the morning".
Maybe standard psychological testing could generate more insight into this "waking" quandary? An introvert (internal?) vs. extrovert (external?) or depressed (inernal?) vs. manic (external?) poll might generate a correlation.
Have you used your electrodes to investigate your brain patterns on awakening? If you have Tinnitus on awakening, what happens if you zap your brain before awakening?