The driver is responsible for maintaining control of the car at all times, so they will get the ticket even if they're using FSD.
There is an argument that Tesla is releasing products that are fundamentally unsafe, and they may be open to some torts there. Of course, Tesla itself would likely point to some language in some agreement that basically amounts to "you're an absolute fool for thinking that our FSD product is any good, and have no ability to sue us for releasing dangerous products;" they've historically been very aggressive in arguing that they bear no responsibility in any FSD or Autopilot crashes.
I think the only company who takes liability when you use their self driving feature at the moment is Mercedes, and it is only active in very specific driving situations.
The auto manufacturer, as they're the entity actually operating the vehicle. You can absolve yourself of responsibility with enough legalese "self-driving doesn't work, it will kill your kitten, you're responsible when you plow though a Denny's" but it doesn't make it right. Mercedes is taking liability, it's possible.
You have no control over how your car's self-driving operates, you can take over control but that doesn't mean you're driving. You're the passenger in one of those student-driver cars, you might have your own steering wheel and brake but it doesn't make you the driver. The life-guard isn't the swimmer.
