Hi Ray
I'm not sure how you have set up your dashboard, but I created a simple test site to confirm it works, so let me outline what I did so that you can compare it to your own experience.
I have a site with a CPT "Things". I have Things posts created by the admin user and by a user with the subscriber role.
I edited the Relevanssi settings so that the index includes Things posts (and updated the index).
I brought the Things post type under Access control, and for the subscriber role gave them the ability to publish posts and to edit and delete their own posts, as well as read rights to be able to view any Things post.
For the "dashboard" I set up a View to display Things posts.
I added a Query Filter for the post author to only show posts authored by the currently logged-in user.
I added a text search field that searches title, body and custom fields, and a submit button.
I inserted this View on a page, my dashboard page.
I visited the page as admin and saw the Things published by the admin.
In another browser I logged in as the subscriber and visited the same page.
I saw the Things published by the subscriber. I searched for content that exists in their Things and the results updated as expected.
I searched for words that only occur in the admin's Thing posts, and go "no results found".
So my experience is that it works as expected.
Based upon the above can you clarify what you are doing differently?