The way the speaker enunciates н in сын is definitely confusing. I hear an m, not an n. But the speaker pronounces сын and сыновья consistently throughout the course, so I suspect н is indeed pronounced as m in сын and сыновья. It's just another "go figure" oddity, like the way ты, вы and мы don't rhyme.
That said, it's rather presumptuous for an English speaker like me to complain about the vagaries of Russian pronunciation. The rules of English pronunciation (if indeed there are any) are much more opaque, convoluted and rife with exception than any other language could possibly aspire to.
the hardest part of russian for me is avoiding pronouncing the "ь" (bc its silent) and then trying to figure out whats a "ь" and whats a "ы" and i end up messing up the pronunciation