My guess is that the increase in temperature already crossed the limit at which the radiator can sustain, so it just blew and you didn't see any rise in coolant temperature. However, if the radiator was still good, you would have seen the temperature rise above normal during that climb, and then subside back to its normal reading once you're back on level ground.

Uphill drives usually strain the engine more. Another thing is if the engine is not used to the climb, or not used to being pushed and then it was your first time to do so after years of normal city driving, then binigla mo yung makina and its cooling system. Cars love to be driven.

It's actually not a classic example of overheat, but a classic example of radiator failure. It happens, it's happened to me when I took our 1.3L Corolla '95 model year on a spirited drive back home. The car is not used to being pushed and it's very hard to get some decent power out of it, so when I tried, the radiator blew, minutes away from our house luckily. Parked in the garage and shut her off just in time.

Pretty sure when the radiator top blew, only then did the engine temp gauge read that it's overheating. ;)