Broadly speaking, Cuban origins don't figure prominently within the standard story of the origins of jazz. Jazz is usually considered to have formed in New Orleans out of a variety of influences, but most prominently the turn-of-the-century style of ragtime, which was associated with a certain dance style (the cakewalk), and was usually seen to revolve around solo piano performance. Ragtime had a strong backbeat in the way the left hand of the pianist would rapidly cycle between a bass note and a chord up an octave. Many of the (usually Creole or black) progenitors of jazz saw themselves as doing little more than adapting piano rags, basically, to more of a full band setting - saxophones, clarinets, trumpets, banjo/guitar, often basically as dance music for people wanting to cakewalk.

It was a white band - the Original Dixieland Jass (or Jazz) Band - that seemingly came to the realisation that the style of music had become something else other than ragtime, and which effectively marketed the new style outside of New Orleans, playing a version of the New Orleans ragtime style on tour around the USA and being recorded playing as such in 1917. So there's no immediate, proximal influence on jazz from Cuban music.

However, if we look beyond the immediate origins of the music, we might see a Cuban influence on the conception of jazz. If such an influence was there, you'd be wanting to see Cuban influences on either the ragtime style, or on the melange of styles which black/Creole New Orleans musicians brought to the ragtime style in such a way as to transform the style.

Broadly speaking, the ragtime style came out of black communities in places in the South of the USA like St. Louis, likely influenced by a) various strains of black folk music of the era that are related to what we'd now call the blues, and b) the march style now associated with the likes of John Phillip Sousa. I don't think there's that much of an opportunity for rural black folk music to be influenced by Cuban music in the late 19th century, but could be wrong - there are some disparate influences on the music that you wouldn't expect, such as an influence of Spanish guitar music (the acoustic Spanish-style guitar being commonly associated with the acoustic rural blues, and the style of playing having some clear roots in Spanish guitar music).

Probably if there is a specific influence of Cuban music it would most likely come from the melting pot that is New Orleans, rather than the ragtime side of things. New Orleans sits on the Gulf of Mexico, of course, and is as close as the crow flies to Havana as it is to, say, Charlottesville. However, while New Orleans has a massive cultural influence from the Caribbean, it's not Cuba but instead the geographically more distant Haiti that has had the big influence on New Orleans culture; Haiti's revolution against the French led to an exodus of people from Haiti to Cuba; the war between the French and Spanish meant that the culturally French refugees from Haiti in Cuba were no longer welcome, thus leading them to settle in New Orleans, playing a role in the massive increase of the New Orleans population occurring at the time. So the descendants of Haitians who'd spent time in Cuba before settling in New Orleans almost certainly played a role in the formation of jazz.

As such, a 1997 paper by Christopher Washburne titled 'The Clave of Jazz: A Caribbean Contribution to the Rhythmic Foundation of an African-American Music' in Black Music Research Journal is probably what you're looking for: Washburne argues that Caribbean music styles were a significant influence on jazz.

The New Orleans brass band tradition provides another connection to Caribbean and, in particular, Cuban music styles. This tradition developed from the Turkish-influenced European military bands of the late eighteenth century. In New Orleans these bands served such functions as marching in parades and playing for political rallies, funerals, celebrations, and dance parties. Their repertoire included marches constructed from popular music of the day, such as the tango "Panama" (1911) and "La Trocha" (1897), which included a habanera bass accompaniment both by composer William H. Tyers. To make the music danceable, the meter was shifted to 2/4 time, the melody ornamented, and the rhythm syncopated or "swung." This swinging syncopation may be the precursor to "swing" in jazz.

Similarly, Washburne argues that the presence of 3-3-2 rhythms and variants in jazz (such as the tresillo that you mention) is representative of the influence of, broadly, Afro-Caribbean rhythms on the music of New Orleans - obviously such rhythms are integral to various Cuban styles. Washburne makes the point, however, that these rhythms are likely derived from West African rhythms, disseminated to New Orleans via the Caribbean - not just from Cuba but from other sources - Haiti, in particular, perhaps not surprisingly given the origins of many in New Orleans (and thus has some issues with the phrase 'Afro-Cuban', which is why I'm using the phrase 'Afro-Caribbean' instead. Washburne argues, further, that such rhythms are especially common in early New Orleans jazz - Jelly Roll Morton or Louis Armstrong recordings from the 1920s, for example, and become more diffuse through the history of jazz, as other influences come to the fore. Washburne is also careful to say that the Afro-Caribbean rhythms - what Jelly Roll Morton called the 'Spanish tinge' of jazz - are, as Morton said, a tinge, rather than the main rhythmic flavour of the music (there's other influences on the 'swing' in jazz, too, for instance). It's likely, argues Washburne, that those rhythms came into New Orleans jazz via the descendants of Haitians (who were of course a slave society, with people transported against their will from Africa, and bringing African rhythms with them); but other people with different cultural backgrounds also ended up in the melting pot of New Orleans, and their conceptions of rhythm also had an effect on the music.

So that Washburne article sounds like what you're looking for!