There seems to be a gapin hole in the Dynasty during that period and when i look at the historical times of "no medici ruling florence", that period does not seem to be covered. So it seems Florence was indeed ruled by a Medici during that period. However, Lorenzo II Di Medici died in 1519 and his (illegitimate) son started ruling in 1532.
Who ruled Florence in between? Thanks!
Here is a list of the rulers of Florence.
After the reinstauration of the Medici Rule in 1512, we have
Giovanni de' Medici, cardinal and son of Lorenzo il Magnifico, 1512-1513; he left because elected Pope Leo X.
Giuliano de' Medici, his brother, 1513-1516.
Lorenzo II, his nephew, 1516-1519.
Cardinal Giulio de' Medici, nephew of Lorenzo il Magnifico, 1519-1523 later Pope Clemens VII.
Cardinal Ippolito de' Medici, son of Giuliano, 1523-27, together with Alessandro de' Medici, illegitimate son of Lorenzo II (or rather of Cardinal Giulio)
Italian Wikipedia is a bit richer in detalis. However it seems that the Medici ruled de facto in Florence until 1527, when the Sack of Rome caused such turmoil in Italy that the people of Florence reinstalled the Republic. In 1530 the Medici returned to Florence, and a year later Alessandro was made Duke of Florence, making the official end of the Republic.