Rares won’t show up on the minimap unless there’s been some interaction with them, with the exception of the 2 bosses (see below). Some (I think) don’t show up on the map even then.
Let’s go through them:
Covenant events - These DO NOT show up on the minimap until a player has activated them, at which point they show up as a star. For example, as Kyrian, if Popo is available for the potion patrol, she does not show up as a star even if I’m Kyrian. But once I activate her, she shows up as a star on the map for everyone.
In this case, activating the event is “engaging” it.
Bosses - Konthragz and the Towering Stove Man - these are the guys who emerge from the portal that sometimes spawns after killing a different rare. They DO show up as a star when their portal appears, and there are several waves of adds that spawn from the right before the boss emerges.
In this case, killing the previous rare is considered to be “engaging” these.
The Rift Rares - Silent Soulstalker, Deadsoul Hatcher, and Screaming Shade - These do NOT show up as a star on the mini-map until somebody goes into the rift and yoinks them out.
In this case, yoinking them from the rift is considered to be “engaging” them.
Relic-Breaker Krelva - Krelva, when she spawns, does not appear on the map. However, somebody has to attack her on her spawn island, then fight her on island 2, then fight her again on the mainland. From the moment somebody attacks her on her spawn island, she shows up as a star on the map.
In this case, attacking Krelva on her main island is “engaging” her.
The teleporter rares show up when the teleporter is activated, even if nobody has attacked them yet.
In this case, repairing the teleporter is “engaging” the boss. I guess.
The Supply Carriage shows up as a star when it’s getting ready to leave. It’s the odd man out. The Supply Carriage is the only rare/event that shows on the map without somebody engaging it.
That leaves just the humdrum stuff (Kroke, Floppy the Cave Bunny, Reliwik, and Dominated Protector) who, I think, don’t show up on the map at all.
And then there’s Yorik, who never leaves the rift so how can you tell. But Yorik has like a 30 second respawn so who cares.
Oh, I should also mention Guard Orguluus, who also is permanently in the rift, and doesn’t show up as a star on the map. Also, nobody seems to know about him, even though he drops Archivist research, so… people should go fight him more.