What can be done about a milky residue left on engineered flooring after cleaning?
Oh my. That is terrible. I'm assuming the floor was really unfinished. I'd confirm that because putting harsh cleaners on a finished piece can look like that. I've personally never seen a oil/wax finish look that bad before buffing but I'd say it at least needs to be buffed. More concerning is why they wouldn't oil/wax every inch. It stops well shy of the base boards. If it was unfinished,  every inch needs to be finished or will always look multi colored. The more I think about it, the more I would spend the money to have someone come out that specializes in wood flooring to evaluate it. I don't think your guy has much experience with wood flooring.