There is a possible error in the 1900 census record.
According to most of the other census records, James Allen was born about 1858-59. In 1900, there is a son named "Joe A", who was born Sept 1859. Joseph Albert was supposedly born around 1863 and died around 1866, making it next to impossible for him to be listed in the 1900 census record, therefore, "Joe A" is more likely to be referring to James Allen, not Joseph Albert.