Who said Ashkenaz might be a result of Geirim? Maybe Sephardim are a result of Geirim. Who said originally Yidden had Sephardic traits; perhaps originally Yidden had Ashkenazic traits.
Yidden were in Sephard from the time of the destruction of the first Beis HaMikdash. Whereas the Ashkenazim only came to Europe later after the destruction of the second Beis HaMikdash. So the Ashkenazim were in Eretz Yisroel together with most Yidden longer than the Sephardim, who were in galus much longer.