While this phenomenon of Americans fighting on the Cuban side in internal conflicts goes further back than you might think, from what I've read it never went beyond the occasional American going off to fight. There doesn't seem to have ever been an American battalion in the same way that, for example, the Spanish Civil War and other conflicts generated so many foreign troops that they got their own units.

The earliest case that I know of is Henry Reeve, also known as "El Inglesito" or "the Little Englishman", born in New York in the 19th century. He fought in the first Cuban independence war, known as the Ten Years War (1868-1878), and fell in combat. He is still venerated by Cuban historiography as having balls of steel (in the metaphorical sense), even achieving the rare rank of General before he died.

There were Americans who rose to prominence among Fidel's troops. One case that got particular attention is that of William Morgan who, like Reeve, achieved a very high rank in the revolutionary army (in this case that of Comandante).

However, his case and that of Reeve are notable to Cuban historians exactly because of how exceptional Americans fighting on their side was. Lots of Americans sent aid, of course, ranging from food to munitions. Many lobbied congress to change US policy. But going down to Cuba, donning fatigues, and fighting it out wasn't something a large number of people did.

EDIT: I can't speak for the War of 1895, which turned into the Spanish American War in 1898, since it is the period I'm least familiar with. I remember seeing tombs of American soldiers who had fought in that war in both Santiago and Havana, but it isn't clear if any fought on the Cuban side or if they were simply part of the American invasion force.