Does this camera, which is actually known as a bridge (Fuji S5600), and not really an SLR (there is no mirror), have an electronic viewfinder? if so you should still see a through the lens image. If not it may suffer from parallax. The viewfinder image is exactly the same as is shown on the screen if it is electronic, so it need only be used if conditions are too bright, and the screen cannot be seen. It may be just be foible of this particular model. I have a 9600 and have not noticed this though.
I agree, that's why I bought the Fuji, I think it just takes a bit of practice...I have a 6mega pixel Samunsg without a viewfinder, and it's a nice little camerea, but i'm still finding it strange using a screen.