https://youtu.be/AvFl6UBZLv4 link to the video.
The video is conflating political control with conversion.
Let's take Egypt as an example- the Muslim conquest of Egypt was very swift, as seen in the video. However, the actual conversion of the population to Islam took place over a much longer time period.
This article (warning- pdf autodownload) suggests that Muslims may have become a majority of the population by the 9th Century (just under 200 years after the Conquest) reasoning (p70) that as the last Coptic revolt was in 831, it is likely that after this date the Muslim population was large enough to prevent any future rebellion. However, it also posits that the proportion of 90% Muslim to 10% Copt that became a stable ratio in Egypt was only reached in the eleventh century.
In any case, no matter the exact timeline, the fact remains that the video you show really oversimplifies the situation and conflates conquest with conversion.