You didn't miss anything; the Second Season anime never shows us what happened to Koyomi during the time period of Tsubasa Tiger after the end of Shinobu Time.
In the novels, though, there is a Third Season of stories which take place during the same timeframe as the Second Season. The Third Season hasn't been adapted to anime yet, although it may well be in the future, since they made Tsukimonogatari against my expectations.
Suruga Devil is chronologically the last story in the Monogatari series, but the Third Season explains what Ougi's deal is and shows us what was going on behind the scenes during the Second Season, including what happened to Koyomi after Shinobu Time. I haven't read the Third Season novels, but according to the Bakemonogatari wikia, the story Shinobu Mail from Owarimonogatari Volume 2 covers this period. It takes place between Shinobu Time (which was immediately after Mayoi Jiangshi, and also overlapped with Tsubasa Tiger) and Ougi Formula, the first story of Owarimonogatari. You can read a thorough summary of Shinobu Mail on the wikia; I'll just summarize how it bridges the gap between Shinobu Time and the end of Tsubasa Tiger.
In return for her help during Shinobu Time, Gaen Izuko asks Koyomi to help her deal with an ancient kaii which seems to have a connection to Shinobu. This is why the vampire hunter Episode was in town to meet Tsubasa on the street during Tsubasa Tiger: he was hired by Izuko to help with this job. Izuko also has Koyomi summon Suruga. Suruga meets Koyomi at Eikou Cram School. They have a confrontation with the ancient kaii, which ends when Kako sets fire to the building. Shinobu and Black Hanekawa arrived during Tsubasa Tiger just in time to see the building burning. Shinobu and Black Hanekawa fight a strange creature in the park, after which they get separated. Koyomi and Suruga meet up with Shinobu. It turns out that the ancient kaii in samurai armor is Shinobu's first servant, mentioned in Kizumonogatari. After a climactic confrontation with him, Koyomi sets off with Kokorowatari to save Tsubasa from Kako, leading to the end of Tsubasa Tiger.
So the short answer is that Koyomi was off on a job for Izuko between Shinobu Time and the final scene of Tsubasa Tiger. He was beat up when he rescued Tsubasa because he'd just finished with another battle.