Seeking census enumerator rules regarding dates

When census enumerators asked who lived in the household, as of what date are they asking? For example, if someone was alive on January 1, 18xx but died on February 1, 18xx, would they be included in the census if the enumerator came around on  May 15, 18xx? I thought I read that the "date" of who lived in each residence varied each census. Sometimes it was, "Who was living in the household as of April 1, 18xx." Other times it could be, "Who was living in the household as of March 15, 18xx." etc......

It was my understanding this date changed each time there was a census. I thought the information would be in the enumerator instructions, but I'm having a tough time finding the enumerator instructions online.