When you first start the engine up, the alternator is creating a LARGE drag on the belt because it is trying to recharge the batteries from the starting draw. When it is not producing the maximum amount of power, such as when the engine has warmed up or you are turning it by hand, then there is hardly any drag. I would guess that your alternator, when the engine first starts, is taking 20 HP just to provide the 145 amps of charging current.
I doubt it is a tensioner problem although it could be a glazed belt. They make spray on belt dressing that you can use to check for belt slippage but I would just get a replacement 108" Gates belt, not a Dayco, and change it. I would also not discount an alternator bearing if the noise continues.