Welcome to the forum!
My page on baby turtles is at http://www.fishpondinfo.com/turtles/hatchling.htm
It's pretty common for newborn turtles to want to just stay put, be it under some dirt or in the water in this case. Do you know how old the baby is? They aren't very active for the first few months, living off their yolks and learning what food is.
Make sure that the baby can easily get out of the water. It may be harder than you think to get up on the rock. How deep is the water? For newborns, just a few inches is enough until they figure things out. The turtle won't get ill from staying in the water as long as it's warm enough, the water is clean enough (so bacteria and fungus don't grow; be sure to change it often), and he/she starts to eat. The warmer the water is, the less need the baby feels to get out of the water to warm up.