First, click the link from Mikey's homepage and you can read some great success stories from several people who started with a mop, bucket, brushes and a shop vac.
Before my TM, I used a "Grout Hog" I got off Ebay, brushes, shop vac and a floor machine. The floor machine is key because you can buy a 3M brush (Cobb has them) and use it to scrub and then you can use a buffing pad to remove any sealer that drips onto the tile.
Many people who do tile with a porty use a 1200 PSI hard surface machine with auto fill/dump and a spinner/turbo tool. It is a lot faster than scrubbing and shop vac method but you still have to do quite a hose/chord dance.
By the way, I have the RV360 and
RX20 and use them for carpet only. I couldn't ever see using the 360 for tile but that is just me. TM, SX-12, deck brush, grout brush, mop to apply chems, sealing stuff and floor machine if I need to buff.