Drugs. The only realistic answer is that your girlfriend is part of a drug smuggling ring. Based on the fact that it's a Japanese restaurant, I'd guess heroin, or possibly crack-type Pokémon.
Seriously, though, I'm tempted to modify this question to say "why would a caring boyfriend ask Quora about his girlfriend's suspicious/random/hurtful behavior, instead of simply asking HER?"
For anyone in a waitstaff job, kanoodling with customers is dangerous – you can give the wrong impression not only to your boss/coworkers, but to other CUSTOMERS that you are a flirt/tease. On the flip side, if you know how to flirt effectively, without giving anyone any "big ideas", it's entirely possible to measurably improve your tips by appearing to be single/available, even if it never comes up in conversation.
My basic advice would be this: mention it in passing, not as something that bothers you, but with a curiosity for "how things work", and whether the issue is specfic to her restaurant, culture, nationality, career, gender, family, etc. Oh yeah, and HAVE THAT ACTUALLY BE THE CASE. 😉
If it's truly going to bug you until she quits her job or gets on the PDA train, then I'd suggest a corrective course of individual therapy, or the smoothest possible breakup you can manage.
Why would my girlfriend hide the fact that I'm her boyfriend while she's working in a Japanese restaurant?