"The 1850 Census began on 1st June 1850. The enumeration was completed within five months. " - Source: A Guidebook to American Genealogy
This matches what you've observed about the dates on censuses. The data if taken for example 21st September would be relating to the household on 1st June rather than the day it was taken.
**In the same book:**
"The 1830 Census began on 1st June 1830. The enumeration was to be completed within six months but was extended to allow completion within twelve months"
"The 1840 Census began on 1st June 1840. The enumeration was to be completed within nine months but was extended to eighteen months."