bnrg
I don't have ASME BTH-1-2005, but I think they are saying that the member is loaded in a manor that causes the member to bend about it's strong axis, not that the load is acting in that direction.
"loaded in the plane of the minor axis" means the the load is acting in the "y" axis causing the member to bend about the x-x axis (strong axis). So, yes, the y-y is the minor (weak) axis.
Warren