But the dial-flip itself isn't the trigger, the decloaking merely has to take place before the dial flip
The dial flip actually the trigger. Any time an event is listed in the rules, the activation of the ability/rule is tied to that event. Arguing that before means "merely has to take place before..." is the same as arguing that after can be "Any time I want to after". This is what leads to things like "I use an action and trigger Push the Limit, I'll wait until the combat phase to take my second action."
Can you come up with any examples in the game which go by the sort of timing you're suggesting?