Jason didn't know what to make of you. You showed up in San Francisco a few days ago. The Titans only knew you were in San Francisco thanks to you showing up on the news. Dick, being the man he was, let you stay with them since you clearly didn't have a place to stay.
When the team found out who your dad was, a couple of them wanted you gone, mainly Hank and Donna. And Gar was just straight up terrified of you, thanks to the stories he had heard. The Joker's kid. The Joker's only kid. You had that same green hair and those same eyes...
But your eyes didn't hold that same sadistic look in them. And when you smiled, it didn't hold any malice. And on top of that, you weren’t intimidating in the slightest.
At least, you weren't in Jason's opinion. If he hadn't been told, he wouldn't have guessed you were the Joker's kid, even with all of the visual similarity between you two.
Jason still kept tabs on you, of course. He was certain he could take you in a fight if it came to that, but he doubted it would ever come to take.