When I worked there years ago, yes you were paid a different minimum wage (not none but considerably lower), BUT your employer - this may have been State mandated as laws do vary - had to make sure that your wage + tips at least equalled the regular minimum wage, so if it was a very, very slow day then you wouldn't be out of pocket compared to a standard shop worker.
It also worked as a nice tax dodge - you had to declare your tips for tax purposes, and also to ensure you were getting at least minimum wage. Of course, everyone only declared the bare minimum so everything else was tax free.
I was raking in a fortune as it was a tourist area with an incredibly high footfall. You'd also jostle for the best shifts/best section for tables as tips were a percentage of your checks, so a dinner service for 6 drinking wine was much more lucrative than if you were doing lunchtime and most of your tables were on the rainy terrace.
I worked all summer, partied hard, travelled the East Coast from top to bottom, and came home with a nice sum for the next University year. Happy days!
But yes, basically mandatory - our employer was known for chasing people down the street if they "stiffed" us but it was very rare behaviour. Our rule of thumb back then was "double the tax" for a tip, but I don't know if that still works out now that percentages seem to have increased.