Tried with several ways to upload an interaction to a seconday private Label, changed interaction name, extension name, privateLabelIds property, etc.
The interaction is always populated to the primary private label defined in the user defined in the environment json file.
The only way I was able to upload an interaction to the different private label was by changing the "Private Label:" on user profile. The deploy is not working for other private labels regardless these are correctly set on the "Additional Private Labels:" field on user profile.