Greetings!
With the help of my friends in Throne of Odin kingdom ("Throne of Odin, we have tacos! 
, also a most excellent Kingdom if I do say so myself 
), I would like to share some findings that confirm that minions drop in specific dungeons and are specifically tied to the minionsā salvage relic association (EDIT: 6/29/21 - this section updated to reflect the post-0.35 results)
Some Background:
When I first started running dungeons for the then en vogue Bone Rings, I started to get the sneaking suspicion that perhaps specific minions dropped from specific dungeon chests. I had run Skullkeep about 200 times and I had only gotten 4, maybe 5 specific minions from the chests. I thought at first that the minion drops were like gear; certain minions had an increased likelihood of dropping from specific dungeons. However, as I was farming for the Dwarven Hammer in Clockwork, I had the same result, 4 specific minions as drops the entire time I ran the dungeon. At this point, I decided that I would start tracking these drops. Perhaps over time I could figure something out.
Throne of Odin members assisted me in the data gathering effort and after a while we had a pretty clear picture that minion associations with dungeons did exist. However, with the introduction of ārelicsā in 0.35, as we continued to gather data, the picture shifted again and actually became more clear:
Minion Tracking UPDATED 6/29/2021 - Only post-0.35 drop data included
During the pre-0.35 data collection minions would appear in as many as 3 distinct dungeons and while there was clearly a pattern, there were also one-offs that made it difficult to establish a clear correlation; then came the 0.35 update and the introduction of relics. I decided to check the minions for their upgrade/salvage relic association since these were dungeon-specific and overall the dungeon relic association agreed with the history of minion drops. But it turned out that when we isolated the drop data exclusively to post-0.35 drops, a 1:1 relationship emerged:
Minion Summary UPDATED 6/29/2021
A few comments:
- The peach shaded cells in the relic column indicate that the dungeon associated with the relic has not had a documented minion drop in our collected data so far (post-0.35).
- There are only 6 green minions and 7 red minions compared to 9 minions each in the other colors. I had expected there to be 8 of each.
- There is no emphasis on chest rarity in the data collection or the rarity of the minions; only the occurrence of a minion in a dungeon-specific chest of any rarity (gold+)
Conclusion
The data collected post-0.35 paints a clear picture that the exact manner of minion-to-dungeon relationship is identifiable with itās salvage relic(s). Given that the pre-0.35 data told a different story, I will continue to observe as updates are made to see whether the drop rate pattern continues to be explicitly apparent.
