The relevant article:
ARTICLE 5
Until the completion of the withdrawal of the Soviet armed forces from the territory of the present German Democratic Republic and of Berlin in accordance with Article 4 of the present Treaty, only German territorial defence units which are not integrated into the alliance structures to which German armed forces in the rest of German territory are assigned will be stationed in that territory as armed forces of the united Germany. During that period and subject to the provisions of paragraph 2 of this Article, armed forces of other states will not be stationed in that territory or carry out any other military activity there.
Germany upheld their part of the agreement, the withdrawal went uneventfully, and the agreement was concluded by the end of August 1994.As you can see, it has nothing to do with whether NATO would accept new members or not. Gorbachev and many other top Soviet/Russian officials have directly refuted this myth, see: https://news.ycombinator.com/item?id=43149963