Hey there, I was just browsing old threads and stumbled upon this. I think I have some answers to your questions!

The Alevis are considered a syncretic Shia Muslim group, with a currently predominantly Kurdish and Turkish adherence based in Anatolia. They were prominent because their beliefs were supposedly what the Safavid dynasty followed, and the Safavids used Alevis (or Qizilbash) as soldiers.

So the first major thing to note is while the heterodox variety of ghulat (meaning "extremist") shi'ism practiced by the Qizilbash was prominent during the times of Junayd, his son Haydar and the latter's son, (Shah) Ismail I, it had already slowly began being chipped away at during the rule of Shah Tahmasp, son of Ismail I.

Why is the Shia Islam of Iran today so different from Alevism, then? Iran follows Twelver Shi'ism, which is highly orthodox and distinct from Alevism. If Iran only has a Shia majority because the Safavids forcibly converted the population, then why do Iranians follow a brand of Shia Islam that's so distinct from what Safavids believed in?

To answer this, we need to start by examining what happened towards the end of and following Ismail's rule.

Shiite scholars were invited from Jabal Amel (in Lebanon) and Bahrain to assist in the process of converting the Iranian population and to help ensure its proper application and practice (among both the ruling classes and the people). In the process, these scholars discouraged or outright rejected mystical and folk traditions. Gradually, with state backing, this new ulema formed an increasingly potent political force, as the Safavids transitioned to a centralized empire. Additionally, beginning under Shah Tahmasp, following campaigns in the Caucasus, hundreds of thousands of peoples from the region (Armenians, Circassians, Georgians) were incorporated into the Safavid realm as ghulams (slaves, similar to the Janissaries), converted to Islam and given roles in administration and the military to help check the political influence and power of the Qizilbash. These two processes continued and increasingly diminished the influence and power of the Qizilbash tribes under Shah Abbas I.

Through the Safavid Shahs suppression of the Qizilbash, increasing centralization of their realm and the promotion of new religious, administrative, political and military elites, the once heterodox variety of shi'ism transitioned to a more orthodox form of twelver shi'ism.

Qizilbash in Anatolia mounted revolts against the Ottomans during the reign of Ismail, but all were put down. Following Ismail's defeat to the Ottomans at Chaldiran, Turkic Shi'ite bands had a much harder time moving between Anatolia and Iran. Restrictions on mobility, along with all the changes occurring within the Safavid realm, left the Qizilbash under Ottoman rule physically and spiritually cut off. This in turn led the communities to isolate themselves, which helped preserve their more syncretic variety of Islam!

I hope that answers your questions!

Sources:

The Emergence of Modern Shi'ism: Islamic Reform in Iraq and Iran - Zackary M. Heern

Iran: A Modern History - Abbas Amanat

The Safavid Synthesis: From Qizilbash Islam to Imamite Shi'ism - Kathryn Babayan