Everything is working, your pump's gauge isn't that accurate, your cheapy electronic gauge works pretty well.

Here's what's going on:
When you reattached the pump, the tyre's air is under pressure and it fills up the pump's hose and pressure gauge. Some of the tyre's pressure is lost when it fills up the additional volume of the pump's hose and pressure gauge.

It's just a coincidence that the pump gauge reads 60PSI after you attach the pump.