No I didn't say that apps can be run in sandbox and not terminated in Ask mode, all that Ask mode does is take away the decision if the app should be run/tested by the autosandbox, primarily so that the user can elect to run it outside of the autosandbox.
Anything in Ask Mode run in the sandbox will run virtualised (a Red Border round the Window), so any interactions made or changes, etc. will be lost as the sandbox is wiped when closed. You can't elect to always run this program sandboxed, but when you try to run it the autosandbox would butt in, if you have it set to Ask you can run it sandboxed or outside of it normally (that choice can be remembered), but it still runs through the analysis process.
The Auto Mode just elects to run it sandboxed to do its analysis, this displays a pop-up (see attached image) once it has analysed the program it will notify you of the finding, image2. If at this point you can select how the next execution is handled (sandboxed or normally), but it still runs through the analysis process and the program terminated at the end of the analysis if you selected run sandboxed.
So in choosing Ask Mode, there appears to be an anomaly (which I believe wasn't intended to be in the free version) where it will actually run the program sandboxed - personally, even if it doesn't terminate an application there really is little point in running it sandboxed as when closed everything is history. Any interaction or changes made when running the application are lost. Where in the Full sandbox feature in the Pro and AIS have other settings for running programs like browsers sandboxed and still have some of the changes, etc. saved.