This is more a theoric question then a programming one.
Adobe DTM allows to set a "multiple-domains" list in the property settings and it seems to transfer Visitor Data from the main domain to those added.
I wish to know what practical consequence this settings brings.
How Adobe Sitecatalyst then would know that the Visitor and his data are the same?
The "multiple domains" option actually doesn't affect your visitor tracking. It does affect the cookies DTM itself might set (like if you have a persisting data element), and it changes what options you have if you choose "domain" as a condition in a rule. For visitor tracking across domains, it all depends on your tracking set up. DTM can help set up that tracking (like setting up the Marketing Cloud ID service tool, or setting s.trackingServer) but DTM isn't tracking the visitor directly- it's just hosting the code (visitor ID service and/or analytics appmeasurement code). Check out https://marketing.adobe.com/resources/help/en_US/mcvid/mcvid_cname.html for more info on cross-domain tracking (which is not a concept unique to DTM- as I said, DTM is just the deployment mechanism).