Simultaneous editing of files is generally speaking not possible. It’s essentially always a case of “last change wins”.
And, yes, the broom if red does indicate that the “real” file has not been updated. When you do, please note that it’ll be the last one to update who “wins”.
So, when you’re editing files from different locations, you need to ensure that you’ve really saved (and in the case of AxCrypt, cleaned) on one computer before moving to the other. This is the same principle with, or without, encryption.