The 30-year-old jumped at the chance to join the North-East club, needing no second invitation to resume his working relationship with O'Neill.
"Because he was a player, he knows what you're thinking every moment, what you need every moment and he is very good at reading how you are feeling," said Cuellar.
"He gives you everything you need to make sure you give him everything back. There is good communication and that makes it easy. He has always had a good season wherever he has been. The way he trains and the way you play with him.
"It's enjoyable but there is pressure too with him. He gives you a lot of confidence and you are allowed to do everything you want with your skills and the way you play but there is a responsibility on you to work hard."
Sunderland's first match of the new season comes against Arsenal at the Emirates on August 18.