There was another similar question not too long ago, and there are probably other older discussions under general topics like 'cultural differences / kulturelle Unterschiede.'
My sense is that it's probably more common for English speakers to say 'Make it X' for a relatively short service that's performed on the go, like a cab ride, pizza delivery, etc. In a restaurant where you sit down at a table and have a full meal, you usually don't discuss the tip with the waitperson or round it up; you just wait for the check and write the tip amount when you sign the credit card receipt, or if you pay cash, you let them bring you change and leave what you prefer. If you told a waiter to just round it up, you might need to say something like 'Sorry, I'm in kind of a hurry, can you just make it $16?' One cultural difference may be that waiters may not carry a lot of cash themselves, they may have to go get it from the cash register anyway, so it doesn't really save them any time to tell them in advance.
Rounding up from $13.80 to $15 is close to 10%, so it's not too bad, especially if you look like a student or someone who doesn't have much money, or in a very casual restaurant like a diner. But for good service in a decent restaurant, it would be nicer to give a little more; 15% is now fairly standard, and many people probably now give more like 17-18%. Some waiters, and advice sites that give recommendations on tipping, would even like you to think that it should be 20% or more, but to me that's too much.