The Burmilla is part of the Asian cat group in the UK. In fact, it is the first in the group. Accordingly, it is one of the Asian cats.
I have made a post about the Asian cat on this page: Asian Cat where I discuss it in some detail.
You know I am not sure why the word 'Asian' was selected except that the Burmese is one half of the parents of the Burmilla and the Burmese hails from Burma, in Asia - or does it really? - see There were no Burmese cats in Burma.
The Burmilla is an "Asian Shaded". It includes both shaded and tipped cats. The coat should not be so lightly tipped that it appears white. The undercoat should be pale. Tabby markings should be limited to the face, legs and tail and broken necklaces1.
1. Encyclopedia of the Cat by Dr Bruce Fogle.