My 2018 turbo doesn't have an aux pump, I don't think a single Hyundai/Kia turbo does. It only has the water cooling jacket in the turbo to boil on shut down.
If I have been on repeated high boost before I shut down, which is often. I make sure I have a 1.5 to 2 minute cool down time of at least 1,500 rpm+ before shutting down. Idling won't do it, because of lack of turbo water flow at idle, so while going to the final destination I go to dual clutch/manual mode and keep rpms up, as an example going into a parking ramp.