Dallas,
Let me try a simple visualization exercise for you...
A 'straight' bellcrank doesn't care what angle it rests at when equal weights are hung from both leadout eyes, right? They stay balanced in whatever position because the distances foreshorten simultaneously on both sides.
A 'self-centering' bellcrank has the arms droop below the pivot, and they are usually tilted that way as well. Hang identical weight off each arm, and it will tend to swing back to "neutral" from any other position you try to put it in. And you can see why: swing it one way, and that arm 'gets longer' while the other 'gets shorter.' Identical weight, remember? The longer arm has more leverage, more turning force, until the other arm reaches the position where both are equal in length.
And, as Don B mentioned, the control surface airloads feed back through the pushrod system to help restore neutral quite well. Choosing a 'self-centering' bellcrank is basically a matter of preference, and does not usually make a really important difference.
Now, if you mount it backwards, it would become a 'self-destructive' bellcrank that finds it hard to stay at neutral - tending to lock over anywhere else... DON'T do that!