Shower was leaking, when I removed the tiles, the wood underneath the shower was wet?

The tile guy just wants to add fresh grout, but doesn‘t that wood need to be replaced too. Help the work is to be done in 2 days.

Is this tile in the shower? If so you need to pull up the tile and have a tile membrane installed on the floor to waterproof the area. If it is outside the shower the wood should be treated wood or it will bulge and crack the tile in the future. If it is treated wood then you can just lay replacement tile down. If they know what they are doing and have the appropriate help, then any tile job can be done in one day.