As for as I know, there is no public API for submit event in Qualtrics.
However, in our scenario, we have a survey embedded into a website using iframe, and we want to listen to the user's 'submit' event in the survey and do some additional actions in our app.
When we tried with window.postMessages method to communicate with Qualtrics survey embedded in the iframe, we found when user click the 'submit' button, Qualtrics will post a message with data 'closeQSIWindow', which provides the possibility for us to listen to this user action: register a listener to window's message event and check whether the data is equal to 'closeQSIWIndow'.
Since we did not find any document about this behavior - Qualtrics will post 'closeQSIWindow' when user submit survey and this requires no custom code.
I wonder whether this workaround is reliable?