When Tarquin was first introduced, he was a completely new thread in the story, quite independent of Xykon and the gates. If that had remained the case, then - yes, I think he would have to be dealt with first, before Xykon.
But now he's rapidly (and, I note, willingly) becoming entangled with Xykon's plotline. Which means that even if Xykon personally is beaten, his story won't be over until Tarquin is also defeated. About the only way Tarquin could avoid that fate at this stage is to go home right now and forget he ever heard of Xykon or the gates. But he's far too vain for that.