Blizzard said the opposite, but you are correct on meta achievements. Those parts can be completed by separate toons.
Here is the link to them going into more details on how achievements will work when they are account wideMost criteria are not account-wide
If you start an achievement on one character, you can't then finish the achievement on another (there are exceptions, so please keep reading). We didn't think it made sense for one character to get level 60 and another to get level 20 and then see the "level 80" achievement toast. If you start to explore Thousand Needles on one character, you’ll probably want to finish that achievement on the same character.