Term for a prey animal's recognition that something potentially threatening is looking at it?

On my daily walks I frequently see individual or small groups of cattle egrets. At first I would try to photograph them but they would fly away. This vexed me because they ignored everyone else walking by as well as bicycles or loud vehicles in areas where there were roads.

I took it personally until I realized it wasn’t me or my clothes, but the act of looking at them and taking an interest in them that spooked them.

This even happened at distances approaching 100 meters in open spaces, so I am not sure they could resolve my eyes and determine if my gaze was fixed on them. However, a few non-scientific tests suggested that they seemed to get nervous when I turned my head and looked at them, even though I kept moving. But even if I didn’t look at them but instead continued to look forward, simply stopping and standing in place to take out my phone to snap a photo was enough to trigger them to fly away.

Question: Is there a term for this phenomenon in birds or other animals, not the flying away or fleeing part, but the recognition that something or someone potentially threatening is looking at them and/or may have taken an interest in them? Are there separate terms for responses to motion and responses to a gaze based on eyes or perceived face orientation?

Note: I have noticed a similar phenomenon with Malayan Night Herons as shown in What kind of big bird is this seen walking around Taipei? The individuals I see are more acclimated to people, but I still have to act at least disinterested when photographing them.