Heat the oil in a large skillet over medium-high heat for 1 minute. Reduce the heat to medium and add the onion, cooking until it's soft and a little brown around the edges, about 5 to 7 minutes, stirring often.
Stir in the guava paste, tomato paste, vinegar, brown sugar, star anise, allspice, and curry powder. Simmer until the guava paste has melted, about 15 minutes, stirring occasionally.
Turn off the heat and let the sauce cool slightly.
Discard the star anise; transfer the mixture to your blender and puree. With the motor running add the lime juice and rum. Transfer to a small bowl and set aside, or refrigerate for up to 2 weeks.