You shouldn't need a warrant to report a crime being committed, but you should need a warrant if you're specifically looking through a neighbour's window waiting for them to commit a crime.
Private doorbell cameras (and most flock cameras for that matter) point at mostly, or entirely, public space. Or in case of the former also my own property.
Frankly if I sit on my porch and see thru the window across that my neighbor is beating his wife, should I need a warrant to report it? That sounds ludicrous to me.