Upvote:6
For a schedule change in advance it is always the ticketing carrier (in this case, Emirates) that is responsible for rebooking you after the change.
In a perfect world this would be handled automatically, but when multiple airlines are involved it generally doesn't - especially when those airlines are not part of the same alliance (Emirates is NOT OneWorld, despite your questions heading). I would suggest reaching out to whoever you purchased your ticket from (either Emirates or the travel agent) and asking them to arrange an alternative. It is possible they will contact you, but the earlier you arrange the alternative the better the options may be.
Depending on how much notice you were given of this change and how much you need to change your arrival time, you may be able to claim compensation under EU261.