I think the confusion here is coming from the fact that there are two acceptable methods for rigging a stage bottle.
In the first method, the hose is secured with an innertube, and the second stage is secured with a bolt snap. A second innertube may be added as a backup, and is usually placed over the hose clamp until needed. Note that this is "old school" DIR.
In the second method, no bolt snap is used, and the second stage and hose are each secured with an innertube - actually, the hose is secured with both innertubes - one of them is just snugged up closer to the second stage. Note that this is the method that is described in "Dress for Success".
With the first method, the hose is a little more difficult to deploy (bolt snap must be undone), but easier to stow (only one innertube to fool with). It is also (IMO) a more secure method of stowage, since there is very little risk that the hose can be accidentally pulled loose. With the second method, the hose is very easy to deploy (just pull it out), but more difficult to stow. It could also be argued that the second method is more in the "spirit" of DIR, since it accomplishes the same thing with fewer pieces of equipment.
Depending on when you were taught (and how you were taught), it's entirely possible that you only used the upper tube to secure the hose. In this case, you should have secured the second stage with a bolt snap. If you are using the "two tube" method, then you should be pulling the hose through both tubes when stowing it. Otherwise things will flop around, which increases the risk of entanglement.
So either way, there should be two points of contact - one for the hose and one for the second stage.