Your link does not show this. It is a calculation of the total number of slaves and their population growth rate only. The data from the US Census is pretty similar to what he estimated. It showed the slave population increased by 30.6%, 23.8%, 28.8%, 23.38% decade on decade starting in 1820 and running through 1860. Meanwhile the total White Population grew 34%, 34.25%, 37.12%, 37.53% in those same decades. It is impossible to disentangle the native born White population vs immigrants and/or children of native/immigrant marriages. For slaves however few were imported after 1808 so the population rate increase is a good indicator of birth rate. If the slave birth rate was higher than the White population's birth rate then that was more than offset by immigration gains in the White population. The percentage of the total population which was Black actually decreased over time due to this.
Man, you want to have your cake and eat it too. The immigration gains were in the northern states. Most immigrants settled in the north where the jobs and opportunities were.
The slave population was in the south. By the time of the civil war, slaves represented approximately half the population of the Deep South states. Half! Slaves had twice the birth rate of the white population. That made economic sense to the slave masters… each slave was worth a lot then, but as time went on, it would pose a major problem if they didn’t find new markets to sell the excess to.