Hi Marthe, I've never used a program to link to another tree but I do know that a tree that link to others as a cousin match also inherited everything that was attached as ancestors to the person they linked with. What I encountered recently though was a tree that had linked to numerous other trees and I'm not sure if that their linking to so many other trees might have created the problem.
The tree had multiple "copies" of the same people in it and somehow they were linked together at certain points. If you link to a tree that contains a some of a family already is it possible that the link creates a duplicate of those people? I've attached some examples of the "copying" of the same individuals where they are attached to different mothers or linked to the same family groups as a separate individual. I counted as many as 16 of the same individuals in this tree. In the profile page of the individuals if you clicked on the Ancestry Family Trees in the Source and click on the on the view Individual Member Tree citation it showerd that there were 26 saved trees for this individual alone. I'm wondering if that may have been at least part of what happened to it.
In the only other tree I know that linked to other trees in DNA matching the tree inherited the ancestors which wasn't a good thing and it may not have had the same effect of creating duplicates because it was new material.