Shouldn't it be the other way? The gender staying a girl under boy conditions, until given a shock to then become a boy?

If you go from girl to boy without changing temperature, you are moving horizontally from right to left, crossing the boundary from girl to boy, but without nucliation sites the transition does not occur.

Same with water going left stays water until given a shock to become ice by changing temperature to be supercooled past the transition line.