As the car is running but not hot yet, dump a couple gallons of water on the belt and pulley area. Chirping noise after replacing the waterpump is normal untill all the antifreeze dries up off the belt. Then with the belt on, go back over the 4 waterpump pulley bolts to make sure they are tight.
And to answer your question, the belt should have an automatic tension that does not need to be tightened.