SSL issue when moving accounts

We're attempting to migrate a few accounts from one instance of WHM to another, upon doing this there is no SSL certificate installed for that account, until the AutoSSL process has finished on the new server there is no SSL host for that site, because of this when you go to the site address it redirects you to the first site with an SSL cert it finds. Any reason why it might be doing this? All is fine after AutoSSL has completed but that can sometimes take up to 48 hours.