In order to save the value you set in the reference selector, it needs to be committed to the database. Then, when you re-open the page with the reference selector, you need to retrieve the database record that you committed.
If you can post some screenshots, I can try and provide suggestions specific to your app.
You could create an association between the object with the reference selector and the user object (Administration.Account or a specialization if you use one). On your home page, have a dataview that calls a microflow to get the current user. Inside of this dataview, you can display the object with the reference selector.