Clarification on Trade Program Signup Flow

I’m creating a flow to encourage some customers to enter our trade program.  I’ll be identifying these customers manually and putting them into a segment which will trigger this flow.  I’m not sure if I have this flow structured correctly.  Particularly with the time delays.  I want to send them a unique cupon with an additional discount if they sign up for the list. If they don’t sign up within four days, I want to send a followup, then if they still don’t sign up, move them to a “cold” segement.

With the way I have it currently set up will the first conditional split be the “Yes” branch if they sign up at any point within four days or does it need to be immediate?  I don’t want there to be a delay between them signing up and getting the discount code.