It was more than just "a single predator sighting." The article says it was two drones and one of them crashed, which is a lot more dramatic. They didn't say how close the crash was to the nesting birds. And they didn't say how long the drones were flying around and how they were flying around before the birds decided to abandon. We don't know, perhaps they were buzzing the terns at a low altitude, or hovering for a long time in a way that looked like a falcon.
There's a big difference between a dangerous looking person passing you by on a busy street, and one that's standing on the sidewalk in front of your house, staring at your window for an hour.
Some birds are very neophobic. And some types of birds have less commitment to eggs than chicks -- a new nest and new eggs can be laid, but actual hatched chicks are much harder to abandon. Terns are very social, so a few abandoning their nests might easily lead to a mass exodus.