To endorse the responses from @mwra and @PaulWalters: there is no problem having different people work on a TBX file in sequence, as long as it genuinely is “in sequence.” One person opens it, works on it, saves it, and closes it. Then the next person does the same. (Allowing for inevitable minor delay in Dropbox updates etc.)
But there are serious problems if the same file is open in two places at once, even if one of the instances does not involve any changes and is in “view only” mode. There’s enough background auto-save, update, and maintenance work going on in TBX that you just can’t have the same file open in two places at the same time.
If you stick to old-fashioned “one user at a time” discipline, and wait for the online stored version of the file to sync and update, all will be well.