There's no external way to refresh a query tag other than its natural schedule, short of restarting it. (Reading a tag just gets the latest value--it has nothing to do with execution.) If the query tag is on a tag group or set to periodic, it will rerun on schedule. If set to event mode, it will rerun when some reference it is using changes. Does the reference tag participate in the query tag's SQL?
Consider not using a query tag, but dataset memory tag. Run your query via scripting when necessary, and write the result to the memory tag.