Front pulley question (not Scootworks)

[Frenchy]

When I replaced my stator, a few weeks ago, I had to remove the front pulley to get access to the wires behind the plate, I noticed that the pulley was mounted with the guide lip on the inside of the bike, so I put it back exactly the same way, assuming it was right in the first place.
I also noticed that the pulley would fit with the guide any way, inside or outside...

The other day I was looking at the service manual and noticed that the front pulley was mounted with the guide on the outside

Is this really important, if it fits either way?

So before changing it (lots of work) I am seeking good advice from you mechanically minded experts.

Thanks