A large part of the refugee influx was from Syria and Afghanistan. In the former the situation was partly the result of America, Israel, the GCC Arabs and Turkey supporting the anti Asad alliance.
America doesn't feel the effects of its foreign interventionism to the extent that Europe does, as far as refugees goes, because of the ocean separating the US from the Middle East. So Europe, Turkey, Lebanon and Jordan end up shouldering the responsibility for housing the refugees.
If Europe is forced to take in hundreds of thousands of Palestinian refugees is Vance going to blame European leaders for that? He won't blame his boss and Israel for causing the refugee crisis.