The entire concept of the Warriors of Light in previous games was that they fought to protect the crystals of light. I always interpreted it that way in XIV as well. It's not about what the player's character has or hasn't done; it's about what they fight for. If Hydaelyn beseeches you to fight for her then you are a Warrior of Light.

The fact that Hydaelyn and Minfillia both outright call you by the title should make it pretty damn obvious to be honest. Anyone that got confused about it simply wasn't paying attention to dialogue.