/ˈmɔɪstʃəˌraɪz/ is the usual NA way to pronounce moisturize. Presumably it used to be /ˈmɔɪstjuˌraɪz/ and the /tju/ was palatalized to /tʃə/ - as it was in future, nature, culture.

But boisterous never had /tju/ so the pronunciation /ˈbɔɪstʃərəs/ maybe came about by analogy with words like moisturize, nature, etc.