re-entry from HK

Hi, when flying into china from the US, at check-in they often want to see your flight reservation heading OUT of china as well as in, to make sure they correspond with your entry permit type.

I have a ten-year tourist visa with multiple entries, for 90 days each.
I want to be in shanghai for 4 months, and plan to go to Hong Kong during that period.

Flying to HK counts as leaving the country, and so then i should get another 3 months at re-entry, satisfying the entry permit requirements...correct?

I know the chinese gov't regards HK as a province so i want to make sure they will still count that trip as en exit/re-entry.

thanks for your help!