@ddljohn-- Yes, you're supposed to open your eye, that's how the solution cleans the eye. Are you worried that the solution will burn your eye or something? You don't have to worry about that. The solution that comes with eye wash cups are absolutely safe for eyes. As long as you use the correct rinse and follow the directions on the label, you will be fine.
I use eye wash cups several times a year, especially when I have allergies. I think it works great. Some brands are better than others though, so you might have to try a few to find a good one. I've actually had issues with a few eye wash cups not sticking around my eye properly. The rinse actually seeped through the sides. That's the only issue I've had with eye wash cups.