Germanic lineage arrived from the east?

[Jaska]

“In Denmark and Sweden we show strong genetic evidence suggesting that observed archaeological and linguistic changes are linked to the migration of Iron Age Danes. Based on the genetic heterogeneity of the migrating population and the inability to identify a suitable source population, it appears that between 1500 and 1200 BP was likely the outcome of an amalgamation among several migrating and local groups, comparable to the formation processes among Germanic groups on the continent. In contrast, in Norway, the adoption of Old Norse and similar social changes as seen in South Scandinavia occurred with limited genetic impact from Southern Scandinavian and must have been more cultural in nature. With the exception of a single early Viking sample, the majority of Viking Age Norwegians appear either to carry local ancestry, or to reflect back migrations from Celtic regions of Britain and Ireland. Of note, the border between the East and West Norse languages closely corresponds closely to that of the Southern Scandinavians and Western Scandinavians clusters during the Viking Period (Figure 6).” (Page 37)

Wouldn't that also need to be the case in the east if this is a South Scandinavian-driven cultural/linguistic expansion? I.e in Eastern/Northern Sweden, where it doesn't seem this South Scandinavian ancestry was very widespread until much later than the actual cultural shift. I see they make no equivalence between this expansion and any genetic source population, but they also clearly state that it's centered in the south and linked to "the migration of Iron Age Danes".

In the Norwegian coast, Scandinavian language spread early on: before 500 CE (evidenced by Saami placenames borrowed from already Proto-Scandinavian stage). However, in Sweden the northward expansion did not yet occur in that time frame. Northernmost coastal Sweden was Swedecized only during the 13th century. Even Old West Finnish spread there centuries before Swedish.