'It seems that first we should to divide the participants into two groups.'
--Yes. It is right.
'then the mixed model will be used for explanation.'--But the mixed dimensionality model was applied only to one of the latent class. So, yes, 'if there is no DIF, then there is no need to explain DIF'.
'Whether the number of DIF will be different from the former methods? If there are differences then which one is correct?'
--Good questions. The authors used item property (for example, item location in the speededness example) as well as the results in the previous studies to judge the DIF items, it is really arbitary. It is better to compare the proposed model to some previously used methods. They may not be the same.