Alright, so Spondias pinnata is native to SE Asia, not Jamaica- it might grow there, though I didn't find any evidence of that, but it wouldn't make a ton of sense to call it Jamaika Pflaume otherwise? A lot of people apparently do, judging by google image searches.

Blighia sapida is also non-native to Jamaica, but was imported there early in the colonial period, and has become widely associated with it. It's definitely a potential option.

Spondias purpurea sap contains urushiol, the active chemical also found in poison ivy, so working it could be quite hazardous, giving you not only a nasty skin rash, but also potentially hurting your lungs if you breathe in dust from it. You're, uh, going to want to make sure it's not this before working with it, I think.

Sorry I couldn't narrow it down more!