There is no tightening a loose pulley, something is bad and needs to be replaced as you have found out. There are differences in the 1.8L and 2.4L engine and you do not state which one you have. The 2009 and 2010 Vibes do not have power steering pumps as they use electric motor steering assist for the power steering. Some have different tension systems for the belt and that depends on where the Vibes engine was built. Some have a spring loaded tension-er pulley, that you can find at places like Rockauto Parts, and others use a bolt to tension the alternator as seen here at this link:
http://www.originalmechanic.com/2015/10 ... n-18l.html So do not be shocked if the info you are seeing is different then what you have.
While you are changing the water pump, you will may want to change out the antifreeze, thermostat, hoses, and belt because most of these items you will have loose or off anyways and if the water pump is bad, these other parts don't have long to go either. Watch when re-filling the coolant system so that you get all the air worked out of it. One of these works great :
https://www.amazon.com/Lisle-24680-Spil ... 00A6AS6LY/ just check to make sure it fits your engine and also watch the videos at Amazon on how to use it.