I am a bit sceptic. We know that groups of people arrived in Anatolia at that time and we know that some of these people spoke some form of Turkish. But do we really know that these were Turkic peoples? We may say some Turkic language speaking tribes or tribal groups arrived. There were also many individuals. Perhaps in the beginning the number of the individuals were more than the number of people who arrived in some form of a tribal structure.
By the way, I wouldn't see the Seljuk Empire as a confederation of Turkic tribes of the Oghuz branch. The Seljuks were Oghuz, but they did not organize their empire on such a basis. Likewise, not all the principilaties that came later were tribal. Although it is assumed that the Ottomans were from the Kayı branch of Oghuz, we do not really know if this information is correct. We do not even know that we could define them as an Oghuz tribe.
What these people called themselves is important. If they didn't see themselves as Turks then we cannot say that they were Turks. If those who arrived in Anatolia didn't think themselves as Turks then Turks didn't arrive in Anatolia. Just because these people spoke some form of Turkish and that there is a country called Turkey in the same land that these people arrived in a thousand years ago does not make these people Turkish. Turkishness is a cultural construct. It cannot exist before it is constructed. Likewise, there are no Turks before Turkishness is constructed culturally.
PS. Can I ask why you are interested in Turkish or rather Turkic history?