What you described actually sounds pretty normal. When you blow the lines out, there’s always a bit of trapped air and moisture that takes a minute to settle. As the pressure equalizes, those last little bubbles work their way up through the water before things fully seal off. It doesn’t necessarily mean your plugs failed or that water is going to sneak back in all winter.
That said, if you want extra peace of mind, you can double-check a couple of things: make sure the plugs are snug and seated properly, and add a dab of pool lube or Teflon tape on threaded plugs to improve the seal. Some people also like to put a bit of antifreeze in the lines as an insurance policy—especially if you’re in a place with deep freezes. Between that and getting a tighter seal, you’ll be covered even if a little air continues to burp out after plugging.