Many, if not all of the effects, on TemplateMonster can be achieved using Swift3D, 3D Studio Max, and Adobe After Effects (and of course Flash and Photoshop).
Swift3D for more simple 3-D and 2-D vector animations
3D Studio Max for more complex 3D animations - usually raster but can be exported as vector for flash if you have the Swift3D plugin
After Effects for typical video post production effects : lighting, blurs, rotations, etc.
Along with these, many of the artists use plugins for Photoshop (most noticeably EyeCandy for Photoshop and Trapcode for After Effects).
They are masters indeed, and if it is indeed just one person creating the site, there is a lot of experience and TIME needed to get to this skill level. Knowledge includes Flash, Photoshop, beginner ActionScript, After Effects, 3D Studio Max, Photoshop, HTML, and perhaps other programs as well.
And it's NOT enough to know them, you have to learn to apply them correctly to create a *professional* look and feel. It takes years to get to this level.
Adam