short answer.... it shouldn't be leaking at all, get it fixed, fast. It will get worse. A "dampness" is ok, but a drop is a drop, not good. (after typing this, I'm not sure this is making any sense at all, work with me, ok?)
longish answer.., the dirty cream color is the water emulsifying with the grease.
The reason why it doesn't leak "at rest" is there isn't enough water pressure to move past (displace) the grease when the shaft isn't turning.
We are not primarily on earth to see through one another, but to see one another through
Some people are like slinkies: not really good for anything... but you can't help laughing when you push them down the stairs