With a double crank it takes 3-4 clicks of the finger lever to shift from the little ring to the big ring. Any more indicates too little cable tension and/or too much clearance between the chain and left side of the cage in the little ring and largest cog.
When you push the thumb button all the way down to the little ring, you have 1-2 clicks of the finger lever that can be used to trim the FD to the right. That's all it takes to stop the rub.
Campy escape shifters work a little differently. There is only 1 click on the thumb button to drop the chain onto the little ring, but there should still be a trim click on the finger lever for trimming the cage to the right.