The Kurds already forced the Syrians to leave, and that’s one of the reasons the largest percentage of “asylum seekers” (illegal immigrants and boat people) are Syrians.
The EU has made Turkey take them, Turkey doesn’t want them, and one of the purposes of this is to be able to send the Syrians back. Hopefully, there will be a territory that will accommodate both groups, but the Kurds (many of whom are PKK, the militant Kurdish Communist group) will have to settle down and stop their attacks. It works both ways, unfortunately, because everything is so insane there, and that’s why I think Trump was right to get us out.
I think the reason most asylum seekers are Syrians is because there's been a bloody civil war going on all over the country for the past 8-plus years. The Kurds have only been a small part of the Assad opposition.