There are potentially four screens that a student sees after they hit "Stop Recording."
The first screen informs the student that Screencastify is processing the video:
The second indicates that the video has been processed and is ready to be submitted to the teacher: 
From this screen, students can also choose to:
- watch the video they recorded by clicking on the play icon,
- re-record the video by clicking on "Start over,"
- or submit the video by clicking on "Submit."
Once students click on "Submit," they will see a screen like this:
which indicates that Screencastify is sending the video to the teacher's Google Drive account.
Finally, students will see this screen:
This indicates that the teacher has received the video in their Google Drive account.
If your students are saying that they have turned in an assignment, but you do not have their video in your Google Drive subfolder, please ask students whether they saw the fourth "Nice work!" screen, or if they stopped somewhere earlier in the process.