No you don't. When you offer trade points in a certain tree, the other player gets the trade points and the trade points they offer are the ones you get. Trade points are applied randomly to unresearched tech in whatever tree it comes from. So if you give 28 Magic points for 28 Civ points, it means THEY get 28 Magic points and YOU get 28 Civ points. You're not actually sharing techs, you are giving access to certain amount of research points in a certain tech tree.
