Except he already had FTG done and completed years before he even entered office. And Mito didn't teach him anything. That was a stupid thing the anime said. Kushina said the she taught Minato a bunch of dealing techniques.The Second Hokage, Tobimara, developed his own version of the Space/Time Jutsu. Using they knowledge and methods he knows of developing the Jutsu, he must have written the Jutsu in the secret scrolls left for former Hokages.
Naruto holding the Forbidden Scroll
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Side Note: Maybe a "Filler," but couldn't find the Manga Chapter were this was shown.
Orochimaru was only able to gather information from the Hokages "Hidden" room, which gave details of other Jutsu instead of Jutsu created by the Hokage themselves. These is why he probably doesn't know of the Space/Time Technique and of Kyuubi/Naruto's Seal.
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Theory/Speculation: Not accurate
Minato must have looked through the Forbidden Scroll to learn and develop a new Jutsu. He must have stumbled onto Tobimara Space/Time Technique. He probably found that the requirements for the Jutsu were not to his liking so he fit them to his style of combat. Tobimara style was probably a water type, Space/Time User because of his experience and talents of manipulating Suiton. Minato maybe not have Suiton nature so he use the Fuuninjutsu (Sealing Techniques) knowledge given to him by Mito and incorporated them into his very on Space/Time technique called FTG.
If you go back and read the chapter, Naruto got the scroll because he knocked Hiruzen out with the Sexy Technique and used that opportunity to grab it. The lecher. xdI'm still saying Naruto tooked a forbidden scroll, things aren't that serious in Konoha xd.
I'm still convinced that Minato taked at least a second hand knowledge of Tobirama's S/T, but it's okay if you think the same.
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