This happens with any kind of saving at all. There's no difference between the autosave and just saving myself.
I have here 3 save games with all 3 situations setup for you to see the bug(s). I'm missing the going to war one, but will get back to you on that.
Loading game save (mediafire):
I saved this at the beginning of the turn and haven't moved anybody. You can load this one up and see that both my sov and Janusk should have 3 movement points -- due to having a boot that gives them +1 movement point -- but only has 2. To see the game not saving the correct amount of movement points, all you have to do is press "End Turn", see that both the sov and Janusk have 3 movement points, save the game, reload the game, and then see they both have 2 movement points.
Leaving town (mediafire):
You can see here that the sov (he's in the town) should have 4 movement points, but only has 2 when leaving the town (and it only shows 2 even in the town). Again, to see it in action, press "End Turn" first (so you can start on a fresh turn), then make the sov leave the town.
There's actually another bug that I just encountered that you can see in this specific game. Load the save game and the sov will have 2 movement points. Make the sov leave and he should have 1 movement point left. Check the movement points of the two others in town and you should see they have 2 movement points. Now here comes the new bug. Make the sov go back into the city and then bam, the two in town suddenly has only 1 movement point. To see it one more time, make the pioneer leave the town and come back and everybody has 0 movement point. Maybe this is Organized working. But they're not in a party, they're in town and it shouldn't apply.
Joining sov party who has Organized trait (mediafire):
Press "End Turn" first. The sov will have 4 movement points, there are two others in the town, eject them out into the sov's party and you can suddenly see the party's movement points have plummeted to 2.
Also look at this, it partially has to do with this too. Autosave has broken tech upgrades and attacks from enemies that appear in the beginning of a turn.