DUde. Drive the car!
That half cup of coolant that came out from the overflow means that the air pocket already passed. When air gets in contact with hot in a closed environment the pressure increase by 1000%. That's gone now - you should now see the coolant level 3.24mm lower than it was before and that's all there is to it.
RE vacuum; "all" mechanics (in-the-world) use vacuum to refill. Even the cheapest shop you can find in the middle of china use vacuum refill. How the hell would it work otherwise. Come on guys...
As per advice:
"drive it tomorrow stone cold and not refill the coolant and see what it does"
My advice: "drive it EVERYDAY and have fun"
