There is nothing in TBB preventing or hindering execution on AMD processors.
TBB might be perceived as "an improvement over OpenMP", but actually TBB and OpenMP serve different needs based on the development environment, ways parallelism can be expressed in an application, and associated algorithms. In the Section 2 of TBB FAQthere are a few items explaining this in more details. If you do not read it yet, I recommend you to do; search for OpenMP there.
You can read the details of my TBB installation on my AMD system in my blog post "Threading Building Blocks, AMD Athlon 64 X2, and Gentoo Linux."