-I heard my plane will leak this junk all over my hangar for years
Yes, your airplane will weep a bit after treatment. That is normal and proof that CorrosionX is doing its job. 

The solution bonds to the metal in your aircraft and if applied correctly will "seek out" areas that are not protected by existing paint. If it finds its way through lap joints that is evidence that it is working and the spots you can't see are getting covered too.
 
Having said that some novice A&P's will apply the spray way too thick and this results in a big slippery mess. This is a good reason to have an experienced CorrosionX application done instead of your local shop!

A heavy application won't hurt anything. It just makes a mess and costs more in material (I don't charge for material!) There is no benefit to spraying extra solution.
 
Likewise if it's not dripping it doesn't mean your A&P skimped out and sprayed too lightly!  

This is more of an art than a science. Your plane will weep, but it shouldn't be crying and should stop after a month or so. Still, having to clean up some drips is a better alternative than having your spars getting crusty. It's a small price to pay for lasting protection!
 
It's easy to spot the difference between CorrosionX solution and fuel and oil, so this won't alter your pre-flight procedure.

It's important to remember that you won't be able to paint your plane for at least 18 months after a CorrosionX treatment. You can CorrosionX your plane the day after paint! But not the other way around. The CorrosionX will "seep" to every spot the painters strip to bare metal. That's what it's supposed to do! This is something to keep in mind when deciding to get treatment.