It knows what time zone you're in by getting your geographic position, and then looking up the relevant TZ. Doesn't always get the second part right, it has a map of the boundaries but I guess it isn't perfect.

The way GPS works is the satellites fly in a known formation, and broadcast a very accurate time of day. Your receiver (Edge 130, watch, phone, whatever) tracks multiple satellites and does a lot of math to figure out how far away each one is by the amount of time it took the signal to arrive. A side effect of this process is that your GPS knows exactly what time it is.

That's why just going outside and getting a fix will set the time.