Semmi did move their things – but only those things that Akeem was referring to in the context of the situation. Akeem said that statement to Semmi, but you have to consider the context of the line. The context includes the following:
- Akeem took the apartment in the first place because he wanted a place that was poor. Remember he told the cab driver to be taken to a part of Queens that was “a common part”. The cab driver comically said something like “Sure, that’s one thing Queens has a lot of: common parts”. The landlord described the apartment as something only a blind man could accept (“It’s a shame what they did to that dog.”) Akeem is excited and says “We will take the room!”
- When their baggage was stolen, Akeem says something like “Let them keep our princely robes.” They then comically go buy clothes they think makes them fit in. Akeem goes to the barber to cut his princely hair (a very big gesture of becoming humble in his eyes).
- Semmi turned their apartment it into a high-class, rich-people’s relaxation pad. This is what alarmed Akeem, and drove him to switch apartments with the landlord (who described his place as a #@%&-hole).
- Akeem still intended to show his prospective wife how he lived in order to continue his experiment to find someone who was not a gold-digger, and would love him as a partner in marriage.
So… When Akeem said “Moves our things”, he was referring only to the humble clothes they wore, their humble toiletries, and anything else they procured that would support their cover that they are of humble background. Semmi understood this, and that is what he did as a loyal subject of the Prince. Semmi may have interpreted the picture as something that did not fit Akeem’s cover of being an average guy. (It also fits neatly into the plot of how the King finds out that something is amiss.)