Correct. It'll only fill in the area that you have selected.
Come to think of it, the Fill tool has a "Tolerance" value for the colours that it will change to black, so you might find it easier to simply use the Brush tool and paint inside your selected area with black. (There's always more than one way to skin a cat with PSE....)
Here is a method which offers flexibility where you can easily fix mistakes and refine your changes.
1. Add a blank layer and fill it with your background color. In this example I went one step further to create a studio-portrait type background. I set the Foreground/Background color swatches (bottom of toolbar) to light and dark tan and applied the Clouds filter.
2. Between the 2 layers add a levels adjustment layer but do not make any changes, just click OK.
3. Group the background and adjustment layers and fill the adjustment layer with black. This restores the picture.
4. Set the Foreground/Background colors to their white/black default values.
5. Use the various selection tools to select the subject, feather the selection a few pixels to soften the edges, invert the selection and fill with white. This reveals the new background.
6. Now you can make refinements to fix areas which were not precisely selected (too much or too little). Activate the adjustment layer. Activate the Paint tool and paint on the mask with black to reveal the original picture, paint with white to reveal the new background. Zoom way in for detailed areas. You might want to use a soft brush on the edges of the subject, similar to feathering. Tip: type "X" to toggle between black & white white painting.
Note that the layer grouping similates a "layer mask" which was added in PSE version 9. A layer mask is just that, a mask that can be added directly to a layer so that the grouping thing is not needed. There are several free PSE add-ons you can download to add this capability to your version.