Unless we live in the Assassin's Creed universe, it didn't involve such people at all. Wikipedia's reference to Byzantine insurgents seems to be the remnant of an instance of vandalism in which someone inserted elements of the plot of the video game Assassin's Creed: Revelations into the article (in which the antagonistic faction consists of a fictional Byzantine insurgency aligned with Şahkulu). Previous editors removed the text from the main article but missed what was in the infobox.

Şahkulu's rebellion in 1511 is generally understood along two axes: as an effort by nomadic and semi-nomadic pastoralists (Türkman) in Anatolia to resist the encroachment of the Ottoman state on their way of life, and as part of the messianic religious movements sweeping the region at the time, inspired especially by the rise of the Safavid state in Azerbaijan and Iran.

After the conquest of Constantinople in 1453, and especially after the defeat of the Ottomans' main rivals for power in Anatolia, the Karamanid and Akkoyunlu states, the empire doubled down on its effort to establish a tighter administration over its territories in Anatolia. This entailed carrying out detailed surveys of the land and dividing it into taxable units to be distributed to its cavalry warriors and attached to the demesne estates of the sultan or his high officials. Tighter government control meant more efficient and regular taxation, which was especially irksome for pastoral peoples used to dealing with weaker states or with states dominated by themselves. While the Ottomans didn't try to eliminate pastoral nomadism by settling the Türkman and transforming them into peasants (that would come in later centuries), they did try to control their seasonal movements and integrate them into their systems of taxation. Thus, for example, they had to consent to Ottoman administrators counting their flocks of sheep in order to assess how much of the "sheep tax" (adet-i ağnam) they would be obliged to pay each year. With the rise of the Safavids, opponents of Ottoman rule saw in them an alternative, and many hoped that a much lighter form of Safavid rule would replace Ottoman administration in Anatolia. At the same time, the Safavids with their so-called extremist (ghuluww) Shii leanings appealed to the more heterodox among the Türkman, some of whom even viewed Shah Ismail as a manifestation of God. Ismail was therefore both the key to breaking free from Ottoman rule, and a messianic figure who would bring about a new golden age on earth. Şahkulu ("The Slave of the Shah") claimed to be acting on behalf of the Safavids in order to bring about this reality. In effect, this was a rebellion rooted in the political and religious conditions of inner Anatolia, and had nothing substantive to do with the Byzantines.