No. The seats just rotate in. Each current member of the Council serves out the rest of the term to which he or she was elected, and then must run for re-election in the districts. It potentially gets a little more complicated if two councilmembers are paired in a single district, but everybody still serves out his or her full current term. As part of the establishment of City electoral districts, the Council will determine the districts that will have an open seat at the 2020 election.
The City Council will be determining the sequence of elections as part of the process of establishing the voting districts.