Dye Sublimation to tile is some pretty cool stuff. I used to make full murals with the process which progressed into a manufacturing company specializing in frames for mounting the tile murals in.
Dye sub is a process requiring a polyester base material on the tile and it is best left to the pros. We all dislike the cost of pre-coated tiles, and for many of us, the cost of shipping such heavy material, but....it is the only way to go.
Great colors are possible and can be quite lovely. Now the bad news....dye sub is not UV safe and therefore must be used indoors and away from direct sunlight...and it can be scratched. Grouting must be done with sandless grout, and gentle. Also, one must not use the old scrub pad or powdered cleansers...something like windex and a soft cloth is best.
One can also purchase glass tile, sublimation ready and in this process, you actually transfer to the back of the glass and therefore it is scratch proof once installed. Still UV unstable though.
The only durable, UV safe process currently on the market is waterslide decals that can be kiln fired. Fortunately, progress is being made in that we can now print the decals on special laser printers. Still some hurdles, but coming along just fine.
Doug