The core members of Urge Overkill are Nash Kato and King Roeser, who both sing, play a variety of instruments, and write songs. Their drummer at this time was Blackie Onassis.
In a 2022 Songfacts interview with Kato and Roeser
, Kato, who handles lead vocals on the track, explained how "Sister Havana" formed: "It sounded like a hook: 'sis-ter Ha-vana,'" he said. "Then the lyrics more or less wrote themselves. We didn't have any firm stance on America's relationship with Cuba, but it sang well and sounded like a hook. There was no political commitment.
Roeser added: "In hindsight, you can see it as Urge's first foray into geopolitics. The protagonist, Urge, or the US, is trying to woo the woman, who could be Cuba."