You were getting older, that meant you were becoming a lot more mature and independent and Aventurine couldn't lie, he'd feared this for years but now you were wanting to go out with your friends, of course he knew that he could protect you no matter what so he agreed.

Before you went out he came over and handed you one of his 'gambling chips' which was actually a tracker, this was your first time being in the city with just your friends and he wanted to be sure you were safe and could come to your aid if needed. If he could he would've gotten some IPC lackeys to be your bodyguards but he thought that'd overwhelm you and your friends so instead he chose to give you the tracker.

While you were out he constantly made sure to check the trackers location and make sure you were safe and he was glad to see that you were remaining in the city centres shopping centre.