Copyright (under US law) is for creative acts. The creativity in a photograph is things like setting up the shot, framing it, choice of subjects, lighting, angle, aperture, focus, etc.

If there is no creativity, there is no copyright. See Feist.

So the delay, and even who presses the button doesn't matter; the only thing that matters is who is responsible for the creative aspects of the photograph.

And, in this case, whether a non-human can, as a legal matter, create an "original work of authorship".