I think it is easy to remember this way:
1. Specular is the
color light that reflect out. So you can paint it to any color except black, whick is not reflect.
2. Specular alpha is the
strength of the reflection. The white reflects more than black.
The way you do alpha channel of specular (not alpha channel of diffuse, they are not the same, the wall (white area) will reflect more than the windows (black area). You need specular alpha in specular texture. You cannot use diffuse alpha in specular alpha.
I spent a few min. to modified you picture here to help more understanding
Specular texture has its own alpha channel. The diffuse texture will tell how the color reflec out. The texture that you have, the model will reflect white color out. You can try painting green to the white glass and the green color tint glass will be. Alpha channel that I add in will make the model reflect just only the window (white area in alpha) and the wall will reflect nothing (black area in alpha). If you want the wall to shine but not reflect, try to paint grey color to the wall in specular texture and stay black in alpha channel.
Diffuse texture has its own alpha channel too. But the alpha here control transparency not the reflection.
Try to play around in a simple model you will get more understanding.
Good luck.
Tic
(PS. I think you should use DXT5 instead of DXT3, I think it compressed more)