After they're little hissing and spitting match when they first met, Azula is keeping a wary eye out for him. If she does see him she'll either put on a fierce brave front or just try and steer a wide path away.

Being frozen in place totally ruined her life once. It's happened to her in nightmares a few times and she's been saved but she doesn't wanna push her luck. Poor Yuri, he probably doesn't deserve to be on her s-list but here we are.