So I had just found an aggressive independent people who had been pestering me on the new continent (I was looking for them so I could start trade and bribes so they would leave me alone.) but I noticed that they were in decline so I just figured I would wait them out, then a few turns later I notice that one of the AIs had taken the city. On reloading the previous autosaves I found out that they took it literally the next turn after I found them. I was in an alliance with this AI and had shared maps so I knew that they hadn't discovered this people before me.

If an Independent People are in the "in decline" state (which as you've observed this one was), they're about to disappear, and any culture that's aware of them can assimilate them by spending influence regardless of level of patronage.

It's a bit rough around the edges and and I do hope that changes in a future release, but that's what happened here.