OK, I've spent about an hour on this and I think I have most of it figured out.
1. When I originally posted, I went back and reproduced it 4 times. This was when I originally posted. I don't remember what the circumstance was but it definitely didn't work and I had the autoplay settings as described. There may still be a bug related to that specific situation but since then it has been working for me as you said, so yeah I guess we can disregard that.
2. The options page for autoplay, this is probably fine, but there should at the very least be a link to the documentation page for autoplay here. The problem is, well, the next point.
3. The documentation page for autoplay; this thing;
I have no idea what this is trying to say. When I was trying to understand what autoplay did, this page actually did more harm than good. Even after reading Stef's post which kind of explains it (which is linked nowhere from the client) I still don't really get this whole name/question/condition/effect. The questions aren't questions, and and a lot of them are terse enough that if you aren't intimately familiar with the card (or even if you are and you don't know what is meant by "question") they don't really mean anything.
It would be much better to describe an in-game situation where this decision comes up, then describe what the client will automatically do for you with each option enabled.
Also, the use of the word "default" is misleading here. Let's take Peasant for example. On this page it says "Peasant's default is [Exchange/Keep]", which suggests that the menu will still come up, but if I just click OK then [Exchange/Keep] is the thing that will happen. This isn't really the desired behavior (and the client doesn't do that, so good) -- I think you should change the wording here to "Peasant will be [Exchanged/Kept]" and maybe even add "without a prompt" if you want to be clearer. Also consider changing the name of the option from "default keep" to "automatically keep" or something similar.
4. The options specific to a given game. Right-clicking on a card to open autoplay options seems like a decent thing to have, but this should not be the only way to set game-specific autoplay options. It's like how you have to hover over your name to see duration stuff, it's a kludge and really isn't good enough to keep around forever.
The best place by far to have these game-specific autoplay options presented to the user is when they're actually making the decision. Every time I have to discard a Curse to a Mountebank, there should be a checkbox near the place I click that says "automatically do this for the rest of the game" or something like that. If that seems annoying, then you could hide it behind some option that is off by default.
Something not as good, but still much better that the current thing and probably easy to implement, would be a button up by the "resign" buttons in the top right which says "Autoplay" and opens up a menu of all relevant game-specific autoplay options. I mean, really this could be combined with the ability to set options during a game which is desperately needed.
5. This is minor, but in my opinion, the groups of options in the options menu should probably be changed so that the "cleanup phase autoplays" are at the bottom. These are the kind of thing that I think people could set automatically thinking they're great, and then wonder why they can never exchange their travellers. This is probably minor though.
In any case, it seems that the actual functionality is there, so now that it's been uncovered, it looks like the quality of my online Dominion life will improve!