I far prefer mopping tile cleaner on than spraying. It doesn't bounce off the floor and get on baseboards, walls and appliances, etc.
Also it's more effective because it is hotter, and you can control it so much better.
I haven't tried that system yet, though. Looks interesting--my guys might even like it. Mike, did you used to spray or use a standard mop (not sure what to call it)? Also, are you dipping in your bucket a lot because it doesn't look like it would hold much solution--but it is nice and wide and can probably get in tight areas nicely--like the toe kick areas.