What I think is going on is that there's a certain date (the beginning of the 7th year: 2231 in DL, 2232 in DA, 2233 in TOA) before which AIs will not ally with each other, similiar to how they won't exchange treaties at first.
Intuitively you are right, but the correct date is 01. January and 4 years into the game (192 turns to be precise).
However, because of the 1-turn-lag an alliance cannot be set up earlier as 8th January of this year.
And because of the new-found ability to align now, the AI will re-evaluate a few factors again, esp. the Military Rating does "weigh" much more heavy than before.
All those changes can be observed very clearly in the Foreign Policy Screen at around January/ February said year.