I don't think Putin is that daft to buy Gulen connection of the attacker stories by the Turkish government. After all, he had a high role at KGB for 16 years. Otherwise why would Russia send an investigation team of 18 to Turkey to investigate the incident? Clearly, "that guy was a Gulen follower who wanted to harm Turkey-Russia relations. Case closed" wasn't enough for Russia.
And it shouldn't be. After the Gulen miltary coup attempt, almost 100,000 people were arrested, maybe half lost their jobs, their passports are taken, from businessmen to people with lower income, whoever had a slight link with Feto had their money in banks withheld, people who are under ongoing investigation were not at their job, be it a teacher or professor, banker etc until they are cleared of those links in investigations.
But this attacker who is 24, who has graduated from Feto schools just 2 years ago and who had an ingoing investigation somehow keeps going to his work, a work that allows him to access weapons,bombs and guns. Moreover, he is promoted to "protection of foreign ambassadors unit" just weeks ago. It simply doesn't make sense and Russia knows this.