From the years from 1790 to 1820, the US census was conducted as of the first Monday in August (August 2, 1790; August 4, 1800; August 6, 1810; August 7, 1820). From 1830-1880 and 1900, the census date was June 1. The 1890 census taken as of June 2. April 15 was the official census date in 1910. The 1920 census was taken as of January 1. Since 1930, the date of the US census has been April 1.
Remember that the official census date may not have been the date that your relative actually answered census questions. It is also possible that your relative was confused because of the difference between the official census date and the date the census taker came to the door.