Am I unscrewing my pump incorrectly?
There are a few possible issues. First of all remember to unscrew the pump head carefully, but that you are probably doing already.

Also in case you have Lezyne pump you should use the Air bleed button to release air before removing the pump head. For other models see the pump's manual.

You should also note the following:

1) The pumps pressure gauges are far from accurate. Try to check the tires pressure with your fingers (in case of road tires with your both thumbs next to each other)

2) The hissing sound you hear when releasing the pump head is not the tire deflating, but air released from the pump.

3) With presta valve (if they have replaceable core) you need to be extra careful not to unscrew the valve core when unscrewing the pump head. If that is a problem you can use glue with the valve core to prevent unscrewing it.