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 face py pressing F. Then they are all facing the wrong way, but you can change that with Alt+N > 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.
//EDIT: Okay, as Robin's new answer points out, of course you could convert the curve back to a mesh if you prefer to have it as a mesh. My bad :D