To try an answer to the original Q: How tight?
It depends on what can happen if there is slackness – how much can you turn one pulley to and fro without moving the other. If the belt drives a cutter, then the slack should be eliminated, and it should in other cases never be slack enough to risk skipping a tooth or sliding over the pulley flange. This latter is more likely (so tension is more critical) if the alignment is iffy, or if it goes iffy under load. This depends on the design details.
Otherwise it is a good idea to try the belt and pulley temperature now and then, and be aware of rubbery smells, which would point to overtight conditions (or overload, mislignment, etc).
Toothed belts are generally more forgiving than roller chain drive, or direct gear drive, but no so capable of really heavy loads.
But as you have discovered, the belt must fit the pulleys.
Regards – Tim