More or less as in the film BUT they were eager to leave the Earth, and they only needed to heed their oath. They do so in a side battle (near Osgiliath IIRC) a

More or less as in the film BUT they were eager to leave the Earth, and they only needed to heed their oath. They do so in a side battle (near Osgiliath IIRC) and, immediately, Aragorn sets them free. But they are not “an army at the ser ice of Aragorn”. They just want to be liberated and to do so, they fulfill the promise they broke. They are not obligated to more (and Aragorn has no power to keep them “here”), much less to make them obey him.