In the 19th century, musicians from Havana and New Orleans took the twice-daily ferry between both cities to perform. The habanera quickly took root in the musically fertile Crescent City. With the work of New Orleans native Louis Moreau Gottschalk, we see the beginning of serious treatment of Afro-Caribbean rhythmic elements in “New World” art music. His symphonic work La nuit des tropiques (lit. "Night of the Tropics") was influenced by Gottschalk’s studies in Cuba.
He used the tresillo variant, cinquillo extensively throughout many of his works. Tresillo is a rhythmic pattern used in Latin American music and is a more basic form of habanera. It’s the most fundamental duple-pulse rhythmic cell in Cuban and other Latin American music. It was introduced in the “New World” through the Atlantic slave trade during the Colonial period. The pattern is also the most fundamental and most prevalent duple-pulse rhythmic cell in Sub-Saharan African music traditions.
Whether tresillo was directly transplanted from Cuba, or if the habanera merely reinforced tresillo-like "rhythmic tendencies" already present in New Orleans music is tough to determine. It is reasonable to assume that tresillo-based rhythms were performed in Congo Square by Caribbean slaves. There are examples of tresillo-like rhythms in some African American folk music such as the foot-stomping patterns in ring shout (a religious ritual) and the post-Civil War drum and fife music. Tresillo is also heard prominently in New Orleans second line music.
Early New Orleans jazz bands had habaneras in their repertoire and the tresillo/habanera figure was a rhythmic staple of jazz at the turn of the 20th century. Comparing the music of New Orleans with the music of Cuba, Wynton Marsalis observed that tresillo is the New Orleans "clave." The New Orleans musician Jelly Roll Morton considered the tresillo/habanera to be an essential ingredient of jazz. Although the exact origins of jazz syncopation may never be known, there's evidence that the habanera/tresillo rhythm was there at its conception.
Fast forward to contemporary times, New Orleans has enjoyed a growing Latin American population since the wake of Hurricane Katrina, when many Latinx folks arrived to help with the reconstruction of the city. With this reinvigoration of the Latin American community in the city, their culture, music, and rhythms have continued to have an influence and meld into the melting pot of Nola music tradition.
*The information above was derived from Wikipedia and news.aag.org.*