I've said this multiple times and apparently it keeps being missed, so pardon me if the following is a bit aggressively framed:
SUPPLEMENTAL CASTING SPEED DOES NOT MEAN YOU CAN USE A JUTSU BETWEEN ROUNDS.
SUPPLEMENTAL CASTING SPEED MEANS THAT YOU ONLY NEED TO USE A SUPPLEMENTAL ACTION INSTEAD OF A STANDARD ACTION TO CAST THE JUTSU.
IN ORDER TO USE A JUTSU BETWEEN ROUNDS IT MUST HAVE THE 'REFLEXIVE CASTING' ADVANTAGE.
The only jutsu that have Reflexive Casting (and can therefore be used between rounds) are MEW and Substitution.