It isn't going to matter which way up you store it IMHO because that isn't juice from the tank, it's condensate.
You know you can hook out those little spacers in the tip? I use the end of a paperclip to pull the two spacers out and dry them off in a tissue. Then give a short, sharp blow through the mouthpiece and any excess will trickle out of the channels on the sides of the tank, then you can push a cotton bud in there to soak up that condensation.
You may be drawing a little harder than necessary if you get a lot of fluid in there, although it's normal for some to form, you can reduce it by making your draw a little softer or slower.
Let us know if this doesn't solve your problem