I guess there is really no right or wrong as to how it works. The grease in the diff can make the differece in being a tight or loose diff. If you run thick grease in the diff then it will be right and those tires won't spin in opposite directions easily. If you use light grease then the diff will spin more freely meaning when you spin one wheel the other wheel will spin the opposite direction easier.

Sometimes new diffs are tighter because the gears aren't worn, while worn diffs spin easier.

I like to use a medium grease lightly packed so that the tires will spin opposite each other but not to easily. If it spins to easily then it is easy for one tire in the back to lose traction and balloon up.