The Raumvirans, ancestors of the Rashemi, are first noted to have settled in what is now Rashemen 5000 years prior to the beginning of the DaleReckoning calendar (Grand History of the Realm
s, page 26).
The Northlanders settled the island of Ruathym "from the west" circa 3100 years before DaleReckoning (Grand History of the Realms
, 29). These people founded Illusk about a century later (ibid.). They're said to have helped found Dambrath in -69 DR after traveling from Ruathym to the Eastern Shaar via a portal (p. 58). Maybe the "portal" was Yggdrasil? Or even Bifrost, which is said to connect Asgard to many mortal worlds.
So yes, it looks like the Rashemi and Illuskans have separate origins.
The Raumvirans were hired as mercenaries in the Orcgate Wars from -1076 DR to -1069 DR, and honestly I'd be tempted to ignore the references to them having been in Faerun 4000 years longer than that and just have them brought through a portal during this period. Perhaps their services were bargained for with Baba Yaga. I can believe the Witches of Rashemen preserved some of Baba Yaga's secrets in their lore. The orcs came through a(n Imaskari) portal from another world at the beginning of this war, so why not the Rashemi? Perhaps the native Raumviran tribes interbred with Kievan Rus, though for this to work the portal would have to not just cross worlds, but also time.
The Northlanders reached Ruathym about 4471 years ago (from 1371 DR), which is about 4859 years ago in Mystara's shorter years (from AC 1010), or approximately BC 3850. Assuming there weren't any timey-wimey shenanigans, if they came to Toril from Mystara they were likely Skandaharians a little more than a century after the events of the DA modules. There's no fan consensus on which Immortal corresponds to Tyr (different fan sources suggest Forsetta
, or Thor, Halav, or Gorm
). If he was introduced to Faerun by Skandaharians from the ancient Blackmoor era, though, Tyr might be identified with Fronaus from ZGG's line. Of course, Tyr could have been introduced to the Realms in another way.
If there are portals in the ocean, I think the tritons might likely have created them, as they're said to have emigrated from the Elemental Plane of Water (Volo's Guide to Monsters
, 115). Perhaps the Skandaharians used tritonic portals to travel first to the Elemental Plane of Water, then to Toril. Perhaps the portal was guarded by the Midgard linnorm