apm-wa, as Koreller stated "City with the status of a province" qualifies it to be tagged with the same admin_level tag on OSM. It does not promote it to be a province, just levels its administrative power. All provinces have welaýaty in their name tag. Ashgabat is a city and no one claims it is a province. There are lot of examples similar to this one accross the OSM where the same tagging has been applied, usually with capital city of the country, which has 2 administrative relations, one that showed its level of power, and another one with the same members which describes it as a city. 

Also, Ashgabat is further divided into districts, as provinces.

Will adding place=city and place=province on these admin_level=4 relations in order to distinguish differences be good enough solution?