To play a little devil's advocate here, were the instances you were casting cure 3 and medica 2 and such ones that required GCD healing like that? Generally you can cover healing requirements with just your off-GCD heals. For example, if there's a multi-hit stack, pop lilybell, problem solved. Maybe the other healer was expecting you to use those kinds of off-GCD heals rather then jump right to the GCD ones?

Furthermore, do you know for sure that the other healer wasn't using their off-GCD Heals? It's possible it looked like they were just spamming glare, but were actually just being efficient and relying on their own + your off GCDs to keep the raid up. Which, especially in Extreme trials, definitely should be the case.