I was playing a new RoG world not linked to SW (but I have SW installed). Upon world hopping through the teleportato, I went to the main menu. The save slot showed the SW icon next to the character portrait. Character selection screen for the new world also had the SW blue background.
The new RoG world was apparently generated just fine, except the fact that Maxwell was nowhere to be seen, i.e. Wilson just spawned in the new world as if he had traveled there by Seaworthy.
After saving and quitting, the SW icon in the save slot changed back to the RoG icon.
Edit: Upon looking at the save slot a couple days later, I realise that my RoG save slot is at World 2-58 (I left world 1 on day 58) rather than World 2-1. Unsure if this is simply a problem with the day counter or if the world is actually considered as day 58 (i.e. hound waves larger on default settings).
I tried to open DS again with just SW disabled to see if it fixed the problem. That just made the RoG icon not appear at all for that save slot. Subsequently creating a new RoG world shows the vanilla DS red background during world gen, but it seems to be generated fine + it has RoG icon.
World hop from RoG -> RoG using teleportato without linking to SW, go to main menu.