The standard is with the roller centered with the arms, it the most aesthetically pleasing, also means the arms are not obscuring the fork when setting up the escapement, and makes visually checking the amplitude easy. As the roller is not poised, it does have an effect on the balance poise. So balances are always poised with the roller in place. For fun, reverse the position of roller and hairspring 180 degrees on a watch with a good rate in the vertical positions. It goes way out. On 3 arm balances it can really be anywhere. If in doubt after replacing a staff, bet on placing the roller jewel opposite where metal was removed to poise the balance.
To highlight that sequence of events I wrote "makes the pallet move", meaning "initiates the movement of the pallet". Of course the pallet also transmits significant power to the impulse jewel and certain parameters can be optimized for a nicely "self starting" mov't, but all that I've omitted for the simplicity of discussion.
I have been searching on (digital) old texts about the importance of this, but haven't found anything so far.
Intuitively it seems to me that with a perfectly poised balance there should be no difference in performances no matter how they sit, but likely there something that escapes me?
Not to say that it would be acceptable for a factory or repairer to assemble in a inconsistent manner, and before considering that three and four spokes balances also exist.