Kickdown Linkage

I have a 65 cuda just rebuilt with 318 and holley 4bbl. My linkage is from old 4bbl 273 and kickdown does not function properly. I still am trying to understand whay it is important. I had trans built so I could potentially race car and shift through gears manually. When driving it runs fine shifts normally through the three gears. The only thing it fails to do is downshift when pushing gas pedal hard. I can manually downshift and run back up to get extra passing power. I am still looking for someone to explain why downshift is important and what it actually does? Please enlighten me! On mine both cables are in place but I do not seem to understand how to adjust this to make downshift work properly? I had a leaking trans line that I got fixed at local trans shop, they told me the same thing about downshift not working properly and it could burn up trans. Again I do not understand this concept? I had a 66 cuda with similar set up and never had trans problems with no downshifting, that car was raced heavily and ran low 14's never had a trans problem, drove that car all the time on street also. Please explain to me how this works and why? My current cuda does downshift when stopping, as at a light it is back into first gear and shifts up as I go when run in D?