Once the application is deleted you cannot access it anymore, as it is not listed in the dashboard anymore.?
Even then you could only see how often the app was used, but not by whom. There is a possibility to add Google-trackers to the app, so you would be able to extract the IPs but I guess you didn't do this.
Maybe you are just too concerned.
You are right, in the very moment the app is published it could be seen by the world, however the chances for this to happen within a day are very low. (Anyone who uploaded a video somewhere and hoping it becomes viral might agree)
- As stated before users could only see what you allow them to see, only the tables, plots, text you publish, not the full-data, or the source code.
- Users need to find the app, the combination of your user-name and app-title. If you didn't already published a list with apps called "App1", "App2", "App3" and someone might be guessing if an "App4" exists chances are small. We already learned shiny-apps aren't listed by search engines (1), as they visit the page just for a fraction of a second and don't wait for the server to be started...
- An User need to see your data is important/ confidential so it can be used (against you), or is of interest for someone else, so it's worth to download the data.
So I wouldn't be too concerned.
Again: As long as your app is online you can check how often it was used, once it's deleted it's more complicated..
(1) How can I make shiny-app appear on search engine? - #6 by ian