Any process that modulates the frequency, rate or extent of postsynapse assembly, the aggregation, arrangement and bonding together of a set of components to form a postsynapse. [ GOC:aruk http://www.ncbi.nlm.nih.gov/pubmed/16672654 http://www.ncbi.nlm.nih.gov/pubmed/16394100 http://www.ncbi.nlm.nih.gov/pubmed/28185854 GOC:bc ]