Let me explain more about DTM:
DTM
According to this page :DTM lets you manage your Adobe Marketing Cloud solutions and other tags across all of your sites, regardless of your number of domains.
Hence it is a tool which helps you in tagging only. In this scenario it helps implement the Target Code.
Any activity within Test and Target will need be worked upon in the Target interface only. I'll request you to have a look at this page for more details.
Thanks
Nikhil