Thank you for your answer.
It seems that it does not resolve our issue as our late test (full order processing) does not link our customer to contact.
Have you any documentation (for mvc implementation) when exactly the link is supposed to be made?
Of course, we can still create the relatiohship manualy with ContactMembershipInfoProvider.SetRelationship(MemberTypeEnum.EcommerceCustomer ...
But as it is supposed to be automatic we fear that create some side effects.