The job being triggered has no awareness of the items in the queue and their inherent priority.
If you want one queue to be treated as a higher priority then in the trigger you can raise the job priority, this should help make sure that job runs first, but it will then complete all the items in the queue, irrespective of priority, before finishing and letting the next lower priority job run and process its queue items.
Queue item priority only affects the next item to be processed from the queue, it has nothing to do with the job priorities.