Affiliation on the papers extracted from the thesis
Your advisor is correct that papers published as a result of your thesis work should include the institution at which the thesis was done as at least one of the affiliations. 

The role of your present institution depends on whether or not you did substantial work on the paper there. If so, then you need to include that as an affiliation as well; if not, then it should be listed as a "Present Address."

What you cannot do is list just your new affiliation, with no recognition of your graduate institution.