That makes sense, since you don't actually set the LineColor property when calling plot (instead you just have a variable with that name).
This means that every time you call this function, the same figure is being reused and a new line is plotted overlapping the existing lines, making it look as if the line colors are changing.
The solution is to do what you intended to do:
LineStyle='-.'
LineColor='m';
plot(t,h,LineStyle,'LineColor',LineColor)
You should also consider using explicit handles: create a new figure (or wipe the old one with clf) and a new axes, use hold on that axes object, plot, and release the hold.
And your use of evalin signals that you should rethink how you handle input arguments.
