Why is 'rester' used in this example (rather than future of s'asseoir) and why is the subjunctive of avoir used rather than subjunctive of finir?

How would you say "Ben will sit at that desk until after he's finished his homework." ?Ben restera assis à ce bureau jusqu'à ce qu'il ait fini ses devoirs.Ben restera assis à ce bureau jusqu'à ce qu'il finisse ses devoirs.