Why? The bijuus can talk through telepathy, Naruto knew that Minato was already coming. What makes you think they didn't just communicate and let Minato use KCM?
That's a lot more believable than Minato figuring out there was such a mode and then somehow defeating and becoming friends with Kurama when they were sealed.
Oh right. Lets just pretend Minato knew nothing about bijuu, jinchuuriki, and sealing techs, I mean, it's not like his wife, who taught him seals, was a jinchuuriki, and it aint like he was the Hokage. Right, a Hokage who is a seal master, and who's wife that he dated since he was 10 was jinchuuriki, wouldn't be able to figure out that there was such a mode. Oh wait......isn't the only reason Naruto has kcm because of Minato? After all, he is the one who designed the seal for Naruto, the one who gave out instructions to gamatora and created the key to the seal, the one who intended for Naruto to master the kyubi, but no, he would have no idea how to unlock kcm and bm mode. Oh my word, isn't he the one who knew from the beginning that love is the key to becoming a perfect jin? By the way, Minato is the one that knew that love was the key to becoming a perfect jin, I could give you MANGA proof if you want. As for defeating Kurama, now you're just trolling, Minato already trolled both Obito and Kurama, what makes you think he can't take on Kurama alone? This is the guy who neg diffed Kurama's TBB, a bijuu's strongest attack and he was about to use a barrier on to subdue Kurama (his own words) before Kushina interfered. Stop rolling bish! Get your facts straight.