I am not sure if I have skipped some chapter, because between Julia ascension (described at the end of 'The Magician King') and Julia teaming with the Brakebills (at the end of 'The Magicians') she should somehow find about Filory, travel to Filory and meet the other travellers, Janet and Eliot, and Josh.
In 'The Magician King' it is mentioned that Julia has met Josh before, during the crossing to Filory, and also some remark is done insinuating she having passed more time there (albeit this could be just a posse/attitude related to her familiarity with nature magic), which could justify why Elliot and Janet team with her. But it also could be simply that they look into the past of Quintin for a suitable partner, or that the dean has been monitoring Julia progress. Whatever, is it described elsewhere?