When you've finished editing a Dropbox file in the Office apps, save your changes and tap the back button. You'll then be returned to Dropbox. The Dropbox app should refresh the file and display your latest edits.
However, if you see a message indicating that you should check back soon, it means we were unable to immediately display those updates. You can either wait on that screen for the updated file to appear, or you can open it in Office again using the Edit button to view or continue editing.
Occasionally, Office may not be able to upload a file in the background after you return to the Dropbox app (for example, if it's a particularly large file or if the file was edited by someone else while you were editing). In that case, open the Office app directly from your home screen and tap the Open tab to confirm whether the file has been uploaded. Once uploaded, you can tap the Export icon next to the filename in Office and then Open in Dropbox to view the file in the Dropbox app.