Copyright and Plagairism Policy for Reviewers of a Rejected Paper
I'm pretty sure that you won't be told who had access to your submission absent a lawsuit, which I don't advise. However, you might be able to instigate an investigation by contacting the conference chair (or program chair,...) of the conference you submitted to. 

You could send both your own work and a reference to the other work you found to the chair and ask for an investigation. The chair knows who saw your paper and might be able to establish an improper connection if such exists. I wouldn't express it as a complaint or an accusation, but simply a request that the committee investigate. 

However, even if such an investigation is undertaken, and it might not be, you might never hear the results. This could be true even if sanctions were applied to another researcher. 

On the other hand, there is plenty of evidence in the history of the world of parallel research and independent researchers coming to the same conclusions nearly simultaneously. Newton and Leibniz parallel investigations that led to the Calculus is a classic example. 

While we like to think that our thoughts are our own, it is usually true that we build on the shoulders of others. The giants that you had access to are also accessible to others. Your insights might be shared, especially in any field that is especially active. 



I'll note that while copyright law varies around the world, your claim of copyright might be weak if your paper hasn't been published anywhere. This might be mitigated if you put an explicit copyright claim in the paper itself, but local laws will determine that.