Do you understand the difference between a colour and a colour space?
As in - colour space, DeviceGray (has one component)
Colour - 0.4
The tint transform is part of the colour space. The tint is not part of the colour space, it is part of the colour. A separation colour space has one component, and that one component is the tint. See PDEColor.
I have not examined your code in fine detail but I can see your tint transform function is wrong. You coded
"{50.0 -128.0 -128.0}" Even if this was syntactically correct, it is a function that returns the same value whatever the input. Your task is to write a function which transforms the tint into a colour representation. In normal cases, the function must return the colour components of the colour when the tint is 1, and white when the tint is 0. Other tints must be transformed to appropriate colours; this of course is not linear for CIELab.