I had wrinkles/dark eyes/puffy face from minoxidil and found no way to avoid it. I tried reducing the dose, I tried changing to the foam, I tried only applying it in mornings so it didn't get on my pillow at night, I tried taking diuretics, drinking lots of water, exercise, skin cream every day, I even tried an alternative called nanoxidil, but alas nothing ended up working.
You can try and reduce the dose but some people just unfortunately get these side effects. And from my experience, the dark circles and puffy face mostly go away but the wrinkles don't. I used minoxidil on/off for about 3 years.