The 3 phase compressor using a 2 pole contactor and a separate 1 pole relay is a cheap and extremely ugly form of "soft start". Essentially, they single phase the motor to get it turning, then close the 3rd pole relay a few seconds later to allow the motor to develop full torque. This does NOT really reduce current, in fact the single phase current is colossally wasteful. But at the 3 phase meter which is averaging all 3 phase currents, it APPEARS to have reduced the starting current because one phase is essentially zero current and pulls the average down! I have seen this done before, I think it is one of the stupidest schemes I have run across. I seriously doubt Carrier did it themselves, I have only seen it done by their dealers or mechanical contractors who are trying to squeeze a few nickels out of a project by not using a soft starter when the HP requires it.
Anyway, time delay or not if you sized the fuses based on the motor FLA you will blow them quite often because the single phasing of the motor, even for just a second or 2, pulls 1.73 times more motor current than it would in a 3 phase starting scenario. The fuses just can't take it.