Naturally, cortman. You don't open Calibre on your second computer, until
after Copy successfully synced itself with the cloud server. Which typically only takes a few seconds.
It's only common sense not to do
anything on that second computer, until all of your files have been synced with the cloud. That doesn't just apply to using Calibre. I have Dropbox, SugarSync and Copy running at the same time, and whenever I start up/wake either of my two computers, I first wait for all 3 of those cloud icons to "stop spinning", and only then I start working on that computer. That way, you ensure there will be no file conflicts in
any software you use.
As mentioned, that wait typically only takes a few seconds. For me, it's not really a "wait" at all, because it has long been my practice to push the computer's start button, and go make some tea.
By the time I'm back from the kitchen, the computer is ready to go. It's a useful practice to proceed in this way, regardless of the use or non-use of cloud sync software. As is well-known, it may sometimes take a few moments for a Windows or Mac computer to
fully "wake itself" from slumber, even though the official start-up/wake-up times proudly advertised by hardware/OS vendors would have you believe otherwise.