I don't think they where ever opposed to direct faction transition. If it made sence.
Malifaux is rightfully owned by Neverborn, however when the path from Earthside to Malifaux opened again all other factions eventually came through and settled or found their places in Malifaux. The same occurance didn't exactly happen the same way the other way around. So while there is clear influence of Neverborn on Earthside now, they shaped themselves in different factions (logically because Neverborn is a collection name of several races that don't all co-operate to begin with).
So not only is Gibbering Hordes a 'Neverborn product' the same can be said for the Everburning man and thus the Cult of the Everburning man . Factions such as The Guild and Ten Thunders are actually much larger on Earthside as they ever where on Malifaux. In that same vein it can almost be concluded that the Arcanists are a movement supported in secrecy by The King's Empire.
Long story short, several of the Malifaux factions are actually just splintergroups of the larger nations/factions that are found on Earthside. So there is a direct transition sometimes.
From the title of the games name you can allready conclude that it's not completely on it's own in terms of it's universe. As 'The Other Side' refers to the other side from Malifaux' perspective. Otherwise it could have been called Earthside instead The system doesn't require the same overlap but the narrative can have that and has that. See it like a game revolving around The Hobbit and a game revolving around Lord of the Rings. They do share the same universe but the games don't have to have the same design, development or system.
Cheers,