No. It won't work that way and it shouldn't. Hype is right the way it works. In case of graphic designing applications, resizing a group resizes all the contents within it. But, in web design context, there are no real groups. The web has <div>. Each group in Hype is basically a <div> and scaling the parent <div> doesn't scale its contents. You have to manually do it. It is necessary because in more advanced projects, groups are a way to mask content.
Hype has responsive options per element. First enable scaling in the scene properties and then, you can set elements to scale.
Add a seperate layout and customise it as needed. You might want to refer to this: Layout for screen rotate (iphone) - #2 by Hrishikesh.