Restaurants can pay you your tips in one of two ways. (1) They can pay you all your tips (credit card, as you would already have your cash tips) at the end of the night or (2) give you your credit card tips in your check.
Usually, if you carry your own bank, you will have your tips at the end of the night. What is really going on here is that the customer is paying you and the restaurant is simply letting you use their credit card machines. You just pay them what you owe them in cash at the end of the night, if it is negative (all credit card pay outs & then they have your tips), they pay you.
As far as claiming tips in paychecks, legally you have to claim all credit card tips regardless of which way they pay you. The restaurant is legally obligated to track the cc tips and give it to the IRS. As far as cash tabs and untipped cc slips go, you are legally obligated to claim at minimum 8% of the tab. The IRS is assuming you will get at least 10% off most checks and lowers it to 8% for the occasional no tip. Well, actually, you are supposed to claim 100%, but...
The restaurant must supply the IRS with the total of cc tips you have received and what 8% of your cash tabs & untipped cc slips are if asked. They do this if you are audited. Big trouble for the tipped restaurant employee whose numbers come in under what the restaurant reports. If the restaurant doesn't track this, they can get in big trouble with the IRS.
OK, I'm done with my restaurant-economics lesson. I just worked in the industry for 10+ years (server, manager [where I really learned how it all works], and event planner).