Your regular house cleaners probably won't get it very clean. They will give it a once over with their mop, which itself may or may not be clean (more likely the mop will not be clean).
When we hired guys to do a tile refresh in our kitchen, years ago, what they did was they had a little spray bottle of cleaner and a brush. They went around doing that. And then awhile later they went around again, this time spraying sealant from a little hand held spray bottle and then wiping. It took them awhile, but it looked way, way better.
I've done it to a bathroom floor and you could definitely do it yourself, but I'll warn you it's a full day on your knees unless the kitchen is pretty small. For other people's mess, as you are describing, I would hire that out, but make sure you pick a company with a good reputation and many satisfied customers online.