Is there a conflict of interest issue if an SEO company employs the services of another SEO company?
I would say that is at least questionable. Especially if they are not transparent about why they outsourced the work they were doing for you. If it was because another company specializes in something they currently don't offer, than it may be okay.
However, if they outsourced all of your work to the other company. Why would not just work directly with the company they sent your work? If this is what has happened, cut out the middleman company and look for cost savings or better communication and interaction with the company actually doing the work for you.