This page describes the compatibility between PolyLang and Domain Mapping System.
Though we don't have a full integration with PolyLang plugin at this point, you can map domains to specific languages defined in PolyLang.
Go to the PolyLang "Languages" tab > Settings > URL Modifications > and select the option "The language is set from different domains."
URL Modifications Settings in PolyLang Plugin
You should then be able to map the domains properly in Domain Mapping System as you choose.