The tensioner is a smooth roller (no teeth) that rides on the smooth outside of the belt. There's a spring pulling it against the belt, but there's a bolt that's supposed to lock it in place. But the squeaking might be a bad bearing in the tensioner. The waterpump pulley has teeth, so it shouldn't slip on the belt...

It almost sounds like your tensioner is loose. Here's how to work the tensioner:
Loosen the tensioner bolt (thru the lower timing cover). Turn the crank counterclockwise a little bit. (3 or 4 teeth on the belt.) This moves all the slack over to the backside of the belt so the tensioner can take up the slack. While you hold some torsion on the crank pulley, tighten the tensioner bolt to lock it in place. You're supposed to do this ever 20k or 30k when you adjust your valve lash.

The timing belt shouldn't be as tight as your alternator belt. You should just be able to twist it 90 degrees in the middle of that long span down the front - between the exhaust cam & the crankshaft.