GSX by default will try to put your airplane reference point (the red cross you see from the Top down view) in the parking center, it can be programmed to apply any offset, even customized for every airplane, but it's something we can do for our airports, were we control everything, including the texture that draws the tee in the first place.
With ADE or AFX, your option is to adjust the parking center, the parking tees are just cosmetic, they don't really "do" anything in FSX, I don't believe the AI system recognize them.