I am not very good in Chinese. But I was told if you are taught the correct way of pronouncing the chinese words from the start, it’ll come naturally to you whether there is an ‘h’ after ‘s’, ‘c’, ‘z’. For eg, we mispronounce words like ‘sheng yin’ as shen yin.
So for those of us who are not pronouncing the words right, I guess have to start memorizing. Don’t think there’s a rule – not that I know of.