Toto gives you plastic inserts to use in the holes that you drill to hold the screws. Many have found that they are a little too large for the hole they tell you to drill. That's annoying. I think maybe they are metric, and chose the closest standard fractional drill bit, so they're a little tight to install easily. You can always substitute any other one that would fit the hole - they're cheap, or figure out what size hole they really need. Now, this may very well have changed...I haven't installed on for quite awhile.
Have you got the unit at home? Take it out of the box, read the instructions, look at the parts, then decide. You can buy a diamond bit at Lowes for probably less than $20...cheaper than a plumber doing it. Depending on the tile, it might take you a couple of minutes per hole. Use a spray bottle and spritz the hole to keep the bit wet and do it slowly - let the diamonds grind the hole - it's not like a knife or a twist drill cutting through wood. Do a practice hole in a spare piece of tile. It helps to put a piece of tape on the floor where you are going to drill.
If you've never used a diamond core bit, you really need a variable speed drill. If you have something with a same sized hole in it, you can place it over the spot where you want to drill the hole, kneel on it, then use it as a guide to get the hole started. If you don't do that, it's a little trickier...the thing doesn't have a center - it is like a pipe with diamonds on the rim, so getting started takes some knowledge. You hold the drill at an angle, around 45-degrees works, and use the edge to score and start the hole. Then, once you get a little divot, you gradually rotate the drill so it is vertical. If you do it slowly and smoothly, you'll get a nice hole exactly where you want. The tape helps grab things and to protect around the tile in case it wanders. Once you do one, it's a piece of cake, especially on a floor...it's harder to hold it exactly where you want on a wall.