Me Information of mobile devices get messed up through my Mac

I am using same iCloud contacts on 2 iPhones, 2 iPads and on my Mac. All with same Apple ID.

On my 4 mobile devices, I can go to settings, contacts, and assign one specific contact to the device as "Me" (Dirks contact for Dirks iPhone, Inas contact for Inas iPhone, etc.....).

So all 4 mobile devices have a specific Me.

As soon as I go to contacts on my Mac and choose a fifth contact an say this is my Macs identity, the identities (Me infos) on my mobile devices get messed up.

Does anybody know, how to assign a contact to my Mac, without messing up the Me infos on my mobile devices ?

Thanks !

Dirk