To give you a brief background about the two creators, Shimamoto and Anno knew each other back in their college days at the Osaka University of Arts, and Shimamoto sees Anno as his rival. Details on the said "rivalry" was detailed in the manga Aoi Honoo (later adapted into a TV drama in 2014) and in the aforementioned Anno vs. Honoo doujinshi.
Shimamoto worked on the said follow-up since August to get the two-part manga to be finished in time, and he was able to pull it off.
[Source: Anime News Network]