Having used the Dropbox/Tbox combo for many years, I entirely agree with this by @mwra. For me it’s just part of the routine when going from one computer to another: saving and closing the files I’m working with in one place, before opening them elsewhere.
Of course it applies to many other file types as well – you wouldn’t want to be editing the very same Dropbox-stored Word document on two different computers at the same time. (I realize that Microsoft has conflict-resolution features that TB doesn’t, and that, for instance, online Google Docs are explicitly designed for multiple simultaneous editing sessions. But I think of file-closing as a standard working-with-Dropbox bit of computer hygiene, as opposed to a specific Tinderbox obligation.)
The good news is that you’re not likely to damage a file or lose info if you have it open in two places. Probably Dropbox will notice a conflict and store the conflicting versions of the file. If edits in one place have overwritten work done on the other computer, you could – if the differences were big enough – use Dropbox’s elaborate version-tracking capacities. That would let you go back and retrieve the conflicting earlier versions and hand-copy any data that might have been overwritten. Don’t ask me how that became part of “my experience”!
Just closing the files, when done at one computer, is the way to go.