on someone's watch
US /ɑn ˈsʌm.wʌnz wɑtʃ/
UK /ɑn ˈsʌm.wʌnz wɑtʃ/

1.
during the period when someone is responsible for something
:
•
The company's profits declined significantly on his watch.
•
I won't let anything bad happen to this project on my watch.