Yes!! You have to cure it! No, you don't cure it in FW. And hitch-hikers are a gamble and hopefully you wont get any bad ones and you will get many good ones. To cure live rock you simply put the rock in a NEW trash can or a rubbermaid bin with preferably 2 powerheads, and a heater. The water should be the same salinity as your tank. (specific gravity of 1.021-1.025). Keep a lid on the bin so as to keep out unwanted algae, You will conduct frequent water changes. 50% every 2 to 3 days would be fine (IME). You will also need to test the water frequently and when your ammonia, nitrates, and nitrites all read 0, then it's time to put it in your display tank.
The freshwater comes in, usually, if you see an unidentifiable crab or shrimp and you can't get him out with tweezers. If you put the piece of rock in FW the creature will bail!
oops- Nemo Lover got there first!!!!