1. You do not "tap in where the cleanout was", unless you also add a fitting to restore a cleanout.
2. You do not normally put the washer trap under the floor since that creates a long riser pipe which could cause the trap to lose its seal from the water's inertia.
3. But that is academic since he does not have a vent on the drain, at least none that shows in your pictures, so the trap will siphon and lose its seal everytime the washer is used.
4. Call him back to do a proper job or get a better plumber.