Was it part of an escape route to Mandatory Palestine or were Jews deported there? I am vaguely aware of Jewish refugees fleeing to Tashkent as there is a database on the US Holocaust Memorial Museum's website.
This is the link to the page of testimony in question: https://yvng.yadvashem.org/nameDetails.html?language=en&itemId=1364159&ind=7
According to the record of your family member, he lived in Przemsyl. Today the city is in Poland and close to the border to Ukraine, but under the Molotov-Ribbentrop pact, the city had the unfortunate distinction of being split down the middle by Nazi and Soviet occupiers.
Large numbers of Polish Jews tried to move to the Soviet zone to escape persecution and massacres by German forces (from what I can tell, it seems like the preferred escape route from here to Mandatory Palestine was though Romania). However, since the Soviet-occupied areas were incorporated into the USSR, the NKVD wanted all residents to accept Soviet passports, which many refugees were reluctant to do, as it seemed a renunciation of citizenship and threatened their ability to return to their homes once the war ended. Unfortunately, refusal to accept a Soviet passport meant deportation, and so refugees from Poland joined other groups from Polish society who were deported by the Soviet government. Some 78,339 were deported in June 1940 alone, and some 84% of these victims were Jewish.
Most of the deportees would have been sent to work camps in Siberia or Kazakhstan. Side note: General Wojciech Jaruzelski, the Communist leader of Poland in the 1980s, was deported to work in mines in Karaganda, Kazakhstan, and wore his trademark sunglasses because of the snow blindness he suffered there. So being sent to Uzbekistan would have been much better, climactically-speaking.
Shafrikan (now rendered as Safrikon) is listed as the relative's place of death, and that actually isn't near Tashkent, but is a suburb of Bukhara. From what I can tell there weren't any major camps in that area during the Stalinist period (it's mostly a cotton growing region), so it might have been a milder form of relocation.
How the Yad Vashem records work is not super clear to me - it says he was murdered in the Shoah, and that his place of death is Shafrikan. If the relative was a refugee from the Germans, and was relocated to Bukhara, and died or was murdered by someone there, I suppose I see how he was an indirect victim, but Nazi forces never made it anywhere close to Uzbekistan, so no one there would have been directly murdered in direct actions as part of the Holocaust.