The positive Z tool length for a tool longer than the one you used to set zero is correct. You are confusing Z height with Tool Height which is properly called tool length. Here is what happens when the tool length gets called. If the tool was shorter than the reference tool and the Z axis was at 2" above the part it would move down until the shorter tool is 2" above the part before a cutting move. Call a different tool with a positive length when the Z axis is at 2" then the Z axis will move upwards until the tool is 2" above the part before a cutting move. This causes more confusion than almost anything else about CNC!
I once worked at a shop where I replaced another guy and he had a huge valve forging in the machine. There was a nice smooth slot cut in the top of the forging about 1/4" deep and 1" wide. I asked another machinist what that slot was for. He said "He always does that. That is Z zero where he sets off all his tools! OMG!!! He clearly had no understanding of tool length offsets. So don't be discouraged, this guy had run the machine for 7 years.