Yeah, this is correct. An aura is just a buff/debuff with a radius - it can also have flags limiting which things in that radius it can affect, but not having the radius means it's just a buff/debuff, not an aura, so the flags don't do anything.
I bet If you somehow gave base aura radius to your aura targets, they'd start projecting the aura too.
This can definitely not happen. The buff/debuff from being affected by an aura cannot itself be an aura, because the two cases use some of the same variables to store different data.