Almost 100% residential grout comes clean with turbo style tool and my TM. Everything except for the 1/2" near the walls, island, ect. I do that by hand. Commercial grout, I sometimes have to prescrub. I use my rotary with a hard surface brush. I have an OP with tile brush, which also works very well.
For the cleaning agent, I use a private labeled product from my distributor. I don't know what it is, but it cleans just about any dirty grout.