Opening pages in new tab of the browser is something you can not control...It depends on the browser and the end user preferences...
Actually Response.Redirect not even support target information...
You may use Response.Write to create a client side JavaScript code to open the link with a specific target, something like this:
Response.Write("<script>window.open('Add_Items.aspx?TestID=1234','_blank');</script>");
Of course this code too, can't ensure opening in new tab only in new window...