You are noticing something that is fairly common - photoreceptor adaptation.
Your eyes contain rods (work under low light) and cones (work under bright light). When you wake at night in the dark, your cones are not contributing very much to your vision initially, then they "wake up".
Some patients seem to have slightly different rates of "waking up" between the two eyes.
The other possibility is that you sleep with the same side down. The lower eye, up against the pillow, may be more completely "in the dark" than the upper eye and therefore has farther to go before it is "awake".
Unless you are noticing definite difficulty seeing in the dark with both eyes, your condition almost certainly does not indicate anything seriously wrong.
Thanks so much for your answer. It helped me feel very relieved.
Kate