en.wikipedia.org/wiki/Pope_Leo_XI

Catholic-Hierarchy’s entry for the 12 December 1583 consistory lists Pope Gregory XIII as the pope who created Alessandro Ottaviano de' Medici cardinal. Separately, the Catholic Encyclopedia entry for Pope Sixtus V states that Sixtus V was elected on 24 April 1585.

Because Alessandro de' Medici was made cardinal in 1583, and Sixtus V did not become pope until 1585, the statement that he was made cardinal by Sixtus V is chronologically impossible. The correct pope was Gregory XIII.

The Vatican’s biographical page for Pius V gives his pontificate as 7 January 1566 to 1 May 1572. That makes it impossible for Alessandro de' Medici to have served "to Pope Pius V" from 1569 to 1584.

Reference works describe Medici more generally as serving in Rome as Tuscan ambassador for fifteen years. For example, Encyclopedia.com says: “For 15 years he served in Rome as the ambassador of Grand Duke Cosimo of Tuscany.” So the problem is the article’s phrasing: it incorrectly ties the whole 1569–1584 span specifically to Pius V, whose pontificate ended in 1572.