Think they're taking stock in how the show has portrayed spies/informants being everywhere. The show has hinted at how easy it is for information, especially info about such a sizable force such as the Vale Army, to get around.
It's not an unreasonable line of thinking given the turmoil of what the North has been going through, especially when Ramsay says "I've been hearing stories about you" or whatever he said, to Jon at the parlay the day before the battle.
Word gets around in the show. No drones needed.