vigilant
/ˈvi-jə-lənt/
adjective
alertly watchful especially to avoid danger
adjective
extremely or excessively vigilant : highly or abnormally alert to potential danger or threat
After an accident or an assault, most people tend to feel unsafe, to have a reduced startle threshold, and to be hypervigilant.
idiom
while being watched by (someone)
The students did their work {phrase}under the watchful/vigilant eye of{/phrase} their teacher.