It all depends on your gut at that moment in the set and the tools you are using and the lens you are shooting with. If I have a follow focus that has a gap when pulling focus I don't rack to the slate and back to the character. This situation only applies when shooting with wider lenses than 50 mm.
When shooting narrower than 50 mm, I always focus on the slate and then rack to the character.
Your job as a focus puller is to have your character in focus. Moreover, your other duty is to give a focus slate so that asistant editor can do his job.
Best regards,
Erol roni Beraha
Focuspuller
Istanbul