Substantiate that...
The zaidi Imamate remained a state for over a thousand years. Vilayat Faqih materialized recently. A totally new doctrine or theology altogether. The quiet school, mainstream Twelver Shi'i belief still exists in it's native Najaf. Heck, it wasn't a state religion till Shah Ismail made it one just a few centuries ago ... Persia or Iran wasn't even majority Shi'i back then...
However that would be post Islam Yemen... prior to that just over 50 years of Persian rule exists, ever. Even Romans tried... in fact Abraha was a Christian, a slave of a roman merchant and when became the king, was an ally of Roman Empire. In fact, Yemen had no reason to accept Persian suzerainty... they were Christian or Jewish... Jewish tribes ruled their parts.