I'm sorry, I don't know what is causing this and haven't found a way to solve it, apart from filling the edges with a faces py pressing <kbd>F</kbd>. Then they are all facing the wrong way, but you can change that with <kbd>Alt</kbd>+<kbd>N</kbd> > _Flip_.

But I guess you don't want to fill the bottom with a face. So here is a workaround: instead of using the outline as a mesh object, convert it to a curve, _Object_ > _Convert_ > _Curve_. This way it loses the modifiers, but after adding the _Screw Modifier_ again it works as expected, all normals have the correct orientation and you can add your _Solidify Modifier_.

Now it's not a mesh object anymore, but at least you can keep it parametric and don't have to apply the modifiers.