Others have explained what “evidence of adequate funds” is in general but for Hong Kong specifically, none of this seem to really matter in practice. Traveling on a European passport, got in by plane, went to Macao and back by ferry, my passport and those of other people traveling with me were stamped quickly every time without asking much or looking at any documentation (not even the return ticket as far as I remember, I think I got a little form to return when leaving).
All this is obviously anecdotal but they did check passports' validity and a Turkish acquaintance faced real problems in Macao because his passport would expire before the end of the 90 days allowed.
I do not know if US passport holders are treated differently but the rules are apparently the same (90 days of visa free stay).