Yes and no.
As mentioned, the colony system in the manga doesn’t have the colonizing nation live with their colony 100% of the time. Instead, the colonizer visits the colony in the latter’s home.
Ex: England visits America at his home. Long gaps of time pass between each visit.

Ex: In his character song “Absolutely Invincible British Gentleman”, England mentions that he has holiday homes – presumably in India and Hong Kong given the lyrics.
“Curry, Chinese cuisine, my holiday houses’ meals.” [x].
What you’ll see is that the word “home” is also used generically to refer to a piece of land/ territory/ settlement. It’s just like how nations will refer to their entire country as their house.
(e.g., “My house [country] has the best food!”)
Another example would be Finland and Sweden’s colonization of America. They make a settlement [home] in America, only to have it taken from them by Holland. In this case, the strip is making a reference to New Sweden, otherwise known as Delaware [x].

