How to make fan power on link to motor move

This is the correct setting, and Klipper does not offer any alternatives.

This is by design. As soon as you activate the steppers, the stepper drivers and motors will start heating up, and this setting is intended to counter that effect.

If you are very unhappy with this behavior, an alternative is the display_template functionality. With this, you could tie the fan control to other conditions like printing, though it is not straightforward and requires some macro coding. See this for an unrelated example; the overarching idea should become clear.