Can you test it now with another file, then walk out of your office/location away from wifi, confirm the test file is there in dropbox with the current time/date stamp on your iphone first, then open the app and test?
One possible idea: it could be that your desktop sync folder may not have completed the process, then AutoCAD360's autosave (out of your control) probably saved the old file it opened, which became the newer file, which your desktop synced with as a newer file.
But do test it out: one file, one anomaly, doesn't make it the norm. See if you can reproduce the problem on demand. I do what you do often and luckily haven't hit this as a problem yet.