Unfortunately the corresponding substitution rules given in Fig. 2 (iii) of the paper are not unique. For some time the exact substitution rules which generate the square level-3-supertile in Fig. 3 of the paper remained unclear. Finally Alessandro Musesti and Maurizio Paolini submitted the correct set of substitution rules in January 2023 to us. Thank you!
Watanabe Ito Soma 12-fold (variant) is another version of this rule with more symmetry.