Yes, 'old' alternator is a GM Delco 10SI series , 3 wire ,bodged so white wire of connector goes to the 'idiot' light on the dash.
The 'new' one, the correct one, MUST have an external regulator to work.
You have 2 options...
1) return the new alternator and get a GM 10SI (same as what was there). should be a simple swap,connect then 'up and running'.
2) keep the correct one, hopefully find the original connector on the engine 'somewhere', pray to the Kubota gods the external regulator IS GOOD. If it is, you're lucky.
I suspect either the original alternator and/or regulator 'died' and it was cheaper to bodge the GM alternator in. MY 'gut' says the regulator is pooched..hate to think what that'll cost.
Whatever you decide, be sure to inspect ALL the wiring and connections. BTW the case of the GM unit should have been rotated to 9 or 3 oclock to prevent water from being on the '1' and '2' terminals.