They warned the move would have a harmful impact on human rights and refugee protection.
Other European countries, including Austria and Germany, are also looking at agreements to process asylum seekers abroad.
It is believed that Somalia and Turkey signing a marine and defence cooperation agreement paved the way for the oil deal.
Dr Mathuki presided over the EAC Secretariat at a time the bloc marking an expansion trajectory, overseeing the entry of DRC and Somalia.
The EU is the largest direct contributor to Atmis, with nearly $2.9 billion since 2007.