The DNA tests just look at haplogroups and mtDNA lineages etc. to make _very_ broad generalizations about what population set some of your ancestors _may_ have belonged to.
It's more likely that at some point in the last 15,000 years someone in your lineage had a child with someone with some Siberian background way far back.
It's more likely that at some point in the last 15,000 years someone in your lineage had a child with someone with some Siberian background way far back.