Tile can handle water. It can't handle soap left behind.
Rinse Away the Soap
How to clean a tile floor so it comes out clean instead of sticky.

Tile is the easy one. It doesn't mind water, so you can mop it properly.
The one thing it does mind is soap left on the surface. Leftover soap dulls the shine and makes the floor feel sticky.
Sweep the grout lines too

Sweep or vacuum along the edges as well as the middle, including the grout lines.
Grout lines are low spots, and dirt settles into them. A mop skips over them, so pick the dirt up first.
Mop with warm soapy water

Mop with warm water and a small squirt of dish soap, working away from the door.
A small squirt is plenty. More soap doesn't mean cleaner, it means more to rinse off.
Go over it once more with clean water

Go over the floor once more with clean water, then let it dry before walking on it.
This second pass is what takes the soap off the surface. It's the difference between a floor that shines and one that feels tacky.
Keep off until it's dry

Wet tile is slippery, so keep the floor clear of people and pets until it's dry.
Get underneath, then finish at the baseboards

Move the lighter furniture and clean underneath. Then wipe along the baseboards.
Dust settles under furniture and along the edges, and the mop pushes it around instead of picking it up.
Short on energy?
Just sweep the grout lines. That's enough for today.
The larger lesson
Tile floors rarely look dull because of dirt. They look dull because of soap. A clean-water pass at the end leaves nothing behind for dirt to stick to.

Soap belongs in the bucket, not on the floor.
