The
Great Seljuks were in fact both Persian and Turkic and none at the same time.
The Sultans and much of the dynasty became culturaly Persian - as
@Shahanshah Rober correctly points out, they spoke Persian, dressed Persian, were inspired by Persian culture, legal and political traditions, their advisors and viziers were in 99% Persians.
When the last Great Seljuk sultan Ahmad Sanjar b. Malik Shah was captured by the Oghuz Turks in Khorasan in 1150's, he viewed those wild Turks as alien to his lifestyle, as have the Persians viewn his Great-grand father Chaghri beg. From this perspective the Great Seljuk Sultans of Persia were culturaly Persian.
At the same time, they still considered themselves Turks and kept some elements of Turkish culture. Reading the Siyasat-nama written for Sanjar's father Malik Shah, we can see that the book's Persian author complains about Seljuks being still too Turkish, relying too much on Turkish clan traditions of splitting the land, that they still favoured the nomadic bands which were devastating the land used by settled Persians.
And these Persian speaking and culturaly Persian Sultans kept refusing those requests of their viziers to get rid of these Tuskish traditions, they continued granting land and protected their wild Oghuz brothers (ironically enough the very same tribes who brought downfall of their Empire).
The Seljuk army was half based on Persian-style mercenary bands, Armenians, Daylamites, Kurds and Greeks and in the other half was the unchained, but very strong Oghuz tribes.
Why did the Seljuks in Anatolia then spread Turkish and not Persian culture? Because those weren't the Sultans. The Kilij Arslan was member of a side branch of the Seljuk dynasty and his sultanate of Rum was based on the unchained Oghuz tribal raiders, not the courtly Persianized Seljuk princes who ruled from great Persian cities of Isfahan, Balkh, Rayy.
Yet, later the Ottomans used a title Padshah and anyone familliar with
Ottoman Turkish language can see that it had as many loan words from Persian as it had from Arabic.... and you can rest assured that most of the Arabic loan words got there because they became part of Persian language.