If the alternator and its belt are pretty new, the belt most likely just needs tightened up a smidge. Common for the belt to stretch and need retightened a few weeks after installation. It's worse when it's cold - rubber not as grippy and there's a high load on the alternator as it's running full blast trying to charge up the battery after cold start. I wouldn't blame the tensioner pulley just yet.

98 Montero, 184k.