Hydroboost/power steering system bleeding

[Barrrf]

I've done the turn the wheel from side to side about a million times. I kept fluid levels up. I can't seem to keep time ps pump from whining though. It's a brand new pump but I'm not ruling it out being bad.

When installing the booster, I had to completely take it apart to reinstall the push rod into the booster body. When the rod piston came out, a ton of power steering fluid came out with it. I didn't refill it, should I have? I assumed it was self bleeding.

Notes: I let the car sit over night and when I first started it, no noise. I shut it off, did some tuning, started it back up and immediate whine again. The whine goes away after about 30 seconds of running but comes back if throttle the pedal a little bit.

Got any pointers?