Sounds like what you have is what is called a "tile-in" sink. These give a very slick finished look, and you can push debris right off the counter into the sink just like an undermount. But much easier than trying to cobble up an undermount installation, which will have a lot of problems to overcome.
In your case the thickness worked out ok, but in most cases the sink has to be shimmed to get the sink lip flush to the finished surface (top) of the tiles. You can use a makeshift screw arrangement or little wooden blocks... get the tiles in, make any final shimming adjustments to the sink, then pack under the lip with bed mortar.