Just because you "catch" yourself doing this upon waking up doesn't mean you are spending a significant amount of time arching your back while asleep. If you are "deeply asleep" how would you know you don't do it then anyway? A sleep study could tell what is actually going on.
I'd suggest experimenting with adjustments to your mattress. Maybe it's too hard (try a mattress topper) or soft (put a board between box and mattress) and
that's actually why your back aches the next day. This so-called arching may be an attempt to stretch away the effects of a bad mattress, not a problem in themselves. If your preferred sleep position has changed for some reason (you were a side sleeper but now end up rolling onto your back) maybe you can counteract that tendency. If you've developed sleep apnea for example, it's possible you're spending more time on your back in an unconscious attempt to counteract the effects.