What tools are being used by companies producing connectable floor tiles?
Graphics on printed tiles (like Settlers of Catan) are done with the same technology as static game boards -- printed on thin paper, which is applied to the backing board with adhesive.  For tiles that have no border (like those for Settlers), or need to interlock, after printing, the tiles, and interlocks if present, are cut with dies -- the same kind of dies used to cut counters for traditional war games, parts for balsa model airplanes, and the pieces of jigsaw puzzles.

Of course, the image printed on the tiles is, as noted in comments, produced with common graphic editing software, either aimed at the graphic arts industry, or at the printing sector.  There are specific methods of ensuring that (for instance) ground texture matches up from one tile to the next, if that matters -- it can be done "manually" with nothing more than copy/paste operations (S. John Ross has a good tutorial on his Risus web site on making maps with very basic graphic software; the same techniques apply to tiles), or there are semi-automated tools for the job.