I agree, there are issues with the requirement of achronicity. Gorard does not use it anywhere in the paper and his foliations in Figures 20, 21, 27 do not respect achronicity of the updates within layers (some nodes are causally related within layers). The requirement is also extremely restrictive to the freedom of foliation, even when proper foliation exists. Including achronicity requirement appears to be a mistake, but it could be I am missing something.
