Your timeline here is incorrect. You forget that the Emperor presided over Nikea whilst he was still in personal command of the Great Crusade. The main accuser against the Thousand Sons was Othere Wyrdmake of the Space Wolves -- who had spent a lengthy time fighting alongside the Thousand Sons and was considered to be (before Nikea) a friend of Ahriman's. The Council did, however, take place shortly after the Emperor had punished and shamed the Word Bearers for their sins of worship via the destruction of Monarchia.
Horus was not yet warmaster and the reason the Khan was not present is never fully discussed, but he did send his most trusted emissary and councilor, Targutai Yesugei to speak in his place. While I do believe that Magnus mentions in passing that he had wished the White Scars' lord had been present, little would have changed. It was quite clear from the outset of the Council that the Emperor was set upon a course that would, at the least, warn Magnus and chastise him from wantonly using his psykic powers or those of his sons.
The Khan, by his very nature, was always on the edge of space and always pushing the boundaries. By the time of the Heresy and the Istvaan Massacre, the Khan had indeed been out of contact for many years -- but that was decades after the council of Nikea.