The partnership started the day of the announcement. I'm sure there's still a lot of things to work out about how it'll work but sending a package over is hardly a sign of them 'hurrying up'.
If the deal works anything like the ABC one did, BBC News may well have access to a CBS server that has all their packages on, and simply selects them for export them to their own playout system.
It is possible (and quite common) to set up newsroom systems to access other servers from other stations/newsrooms, though I'm not sure how fast they can set them up. CBS News uses ENPS
(though I think the O&Os use iNEWS — not sure whether the two systems can interact very much) and BBC News uses ENPS (for now), so it'd be pretty seamless to look at each others' rundowns and video (in theory!). If all that is set up, and set up for maximum ease of use, then a BBC producer could snoop into CBS' rundowns, copy and paste the story, and download the video through ENPS or another system like BitCentral in about 15-20 seconds, all without any communication between that producer and someone at CBS.
If all of that is not set up yet, then at the very least, after planning meetings, CBS and BBC's respective assignment desks are most certainly emailing each other lists of stories that their correspondents are assigned for that day and for when they are slated to air or be finished. A BBC producer could then email CBS and request the story if he or she wants to run it, and then it would be delivered via a more manual way by emailing the script and uploading the video to an FTP server.
TL;DR: it's possible BBC and CBS have already set up their newsroom systems to talk to each other, but even if they haven't, there are more manual ways of still sharing content immediately.