How to combine Views, Rules and EVA to record submission?
I am not familiar with EVA but it looks pretty good.

I have a similar use case with entityform.

You can embed entityforms on nodes using the entityreference field.

Now entityform comes with a view already set up that displays a user's latest entityforms. 

Here is a screencap of the view configuration - it displays a user's latest form submission(s).



You can then add a 'block' version of this view (the 'add' button in the top left corner.)

You can then configure your new block to only show up on the logged-in-user's /user page. 



Hope that helps. Incidentally let me know if you are trying to get the form-fields to be pre-populated with user details. 

Based on your comments: