If the machine takes a single three phase power input, and then splits a leg off to power a separate single phase motor, it shouldn't change the basic power requirement of the machine overall, i.e. 3 phase 220 volts 10 amps... but the machine will then be wired with a neutral as well as a ground (wye as opposed to delta). If you see that the pump motors are single phase, then it is likely you will see a neutral wire in the machine's power tail, to allow 120v single/split phase applications to feed from it. Your VFD will be supplying delta 3-phase, i.e. no center-tapped neutral to allow one leg to supply single phase.
If the pumps are not fed by the same 3 phase input as the spindle motor, and are single phase, then you will see separate plugs for them.
If your machine needs 3 phase wye with a neutral to supply everything from a single source, then you could use the delta 3 phase put out by your VFD to directly feed the motor, and then disconnect the single phase pumps from the machine circuits and power/switch them separately to a single-phase source in your shop.