the thing with the Airbus control system is that you issue 'change' commands to the plane. you issue a 'roll command' when you push the stick to the side, and you issue a 'G command' when you push it forward or back. the plane will remain in the new commanded state until commanded otherwise.
(now read the last sentence again, and chew on it, make sure you understand it thoroughly)
thus, the usual way to fly the plane is to issue small, well-intentioned commands, not to pull on a stick for minutes, as one of the pilots here did. and the plane will stay in the new situation. 'will stay' means that it will issue corrections on its own to maintain the commanded attitude. for example, after having been issued a roll command for a few degrees, the plane will stay in that attitude even of there are disturbing factors - say, turbulence. (as a result, in such a case it is an error for a pilot to try to manually compensate for turbulence-induced attitude changes, as the plane does it on its own anyway, and he will end up over-compensating)
all-in-all, this is a big change in the philosophy on how to fly a plane, even when flying alone, when compared to a 'legacy' system of direct physical coupling of control instruments to control surfaces.
as for simultaneous inputs: actually, one of the pilots can 'take over' command of the plane, and shut out the other one, if he so chooses. none of the pilots did this on this occasion. when having multiple inputs, the plane does signal that the other person is entering inputs as well (at least visually, maybe there is also an aural indication). although, as pointed out, there is no physical feedback on the stick that would signal the other pilots inputs. when both are entering commands, their commands are 'added together'. thus a full pull & a full push on the stick will cancel each other out. two 'small' pushes will results a 'big' push. this makes sense, so that either pilot can 'adjust' the planes behaviour in addition to what is already happening.
the point of not having physical feedback is to reduce strain on the pilots. this way, the stick is always centered, and when moving off center, the pilot knows he's issuing commands to the plane. if it was not so, the pilot wouldn't be sure in which state of the stick is it in a 'neutral' position.
I hope the above gives some background to the story.