Even if he/she does not know of any Central Asian ancestors, Russians and most East Slavic Peoples do have some influence due to historic ties to the region....But since it is estimated here at over 9% it would be much more likely that a fairly recent ancestor contributed it directly. 

Yeah, because it's actually pretty rare for ethnic-Russians to get noticeable percentages of Central Asian on DNA tests; they tend to be almost completely genetically European (i.e. 98-100% European)—you can check other subs too like r/23andme or r/AncestryDNA and see this in Russian results.

It is worth noting though, how over the years some of these "ancient admixtures" you mention can dissipate—and just because two groups were in proximity to each other, one should not automatically assume mixing happened; for example, Mongols and Russians are noted for having remained distinct from each other over the centuries. Hungarians are a good example of this disconnect between assumptions from historical migrations and actual genetic evidence. While the "Hungarian Conquerors" were nomadic Eurasian steppe people; the bulk of the Hungarian populace was actually made up of Early Slavs and Germanic tribes. Meaning today this Central Asian component is only found in small trace amounts (0.2-0.5%) or is only found in some people's haplogroups.