I am not talking about the Ummayad, but the Abbasid's who overthrew them.
Prior to the Saffarid, Khorosan and Greater Iran was ruled by the Tahirid (who were vassal states to the Abbasid), the khawarij, and pagan Zunbils kingdom. The Sunni Persian Ya'qub ibn Layth was the first ruler of the Saffarids, who were independent of the Abbasids. He defeated the khawarij and the pagan Zunbils:
By 873, the Abbasid no longer had a presence in Khorsan and Persia after the defeat of their local Tahirid rulers:
You're correct that Shia were in the northern coast of Iran (Tabaristan) and Qom, but these are not Persian lands to begin with.
Here is an ethnic map of Iran:
In the 16th century, there was two nomadic Oghuz Turkish empires, the Saffavids and the Ottomans. Eastern Anatolia was inhabited by Turkmen nomads who were proto-Alevis(an extreme Shia-like sect combined with Turkish/Pagan pre-islamic culture), they supported the Safavid in fighting and rebelling against the Ottomans. This led to a civil war between these Turks, and the Ottomans invited 13 Sunni Kurdish clans to Eastern Anatolia to populate the region, whilst these Anatolian Turkish nomadic clans left to Safavid territory.
Persians, along with Syrians, were the least Shia group in the Middle East until the 16th century, when Anatolian nomadic turks conquered them and Turkified their region, and forced Shi'ism on them. And from the 16th century until 1923, the rulers, language of court, administration, military, were all Turkish. They imported Shia clerics from Lebanon, Bahrain and South Iraq, because Persians never had any Shia tradition.