Hello Gabriel Arias
If you look at the quick tip of the Tangent constraint, it doesn't support conical faces. See below snapshot.
Using section view and doing the tangent selecting edges on the 2D view is a good option in such cases. This acts similar to sketch curve + sketch curve tangent constraint mentioned in Assembly Constraints Reference Chart. However, I noticed that if I move the screw component and not the body itself, the tangency maintains and the entire assembly moves. If I select the screw body and move it, the tangency condition gets deleted from the Structure tree and the screw comes out of the component. This looks like an issue which I will report it to the development tool.