When you are trying to "scale" the splines you are changing the location of spline points. This will create a new Spline (with different point location and same handle's parameters of previous spline). I don't think you can "scale" this way.
One way is to use the offset entities command. Link the offset function to equations. Suppose your height is 20mm and want to increase height to 25mm just change the offset value in equations to 5mm. If you don't need the original spline down the Design Tree make it as construction line.
few options for you
If you want to use scaling you could say,, create a planar surface and scale that with the scale feature.
Make your sketch into a block and scale that
To scale a whole sketch you can insert a derived sketch and use the modify sketch tool
All depends what works best for you and how you want to control it parametrically.
As an aside I used conics not splines here, they are pretty well behaved