Someone made a good explanation and I'll add onto it.
Minato the Jin
Basically, Minato Sealed half of kurama's chakra inside himself, but he never sealed the fox. When The reaper seal was unleashed, minato was released, but the kyuubi chakra was still within him (essentially making him a jin). This is because, all that's needed to be a jin is for you to have the beast sealed within you. But, when you typically use RDS, you die; except this time, minato was brought back. Therefore, in a sense, he used a jinchuuriki sealing jutsu on himself.
Naruto's KM
Now, lets add onto this. Minato
never sealed kurama inside himself, he only sealed 50% of the chakra. For naruto, he had to play tug of war with the kyuubi to get like 5% of the 50% of kurama chakra inside of himself. Naruto could then entire KM with that 5% whenever he wanted because it was now essentially 'his chakra'.
Naruto's BM
Going on from there, Naruto required co-operation with the kyuubi to enter BM. In essense, they worked in Unison so that naruto would have 100% access to his full 50% share of kyuubi chakra. This allowed naruto to enter a new mode, BM. But, he couldn't attain full transformation as he only had 1 half of the kyuubi's chakra, so the seal couldn't be completely broken. Therefore, his BM looked like what it does, and his full BM transformations simply looked like a giant chakra cloak. But, the essential thing is that, naruto gained access to 100% of the entire 50% of kyuubi chakra inside him -- Not just the 5% he plucked away which allowed for KM.
Minato BM
So, what does this mean for minato? Essentially, Minato has 100% of his 50% share of kyuubi chakra. But, and this is the important part,
there is no fox inside him(unless proven otherwise) to say no. So, Basically, instead of a 5% pool that allowed for a slight bump in power( KCM), minato had access to A very large pool which contained all of the 50% of the kyuubi's chakra. how is this possible? Well, Naruto had to play tug of war with the fox, and the fox held onto some chakra. The fox never completely lost all of it's chakra (it would die), nor could naruto pull it all. But, Minato essential has
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, but on a level where it is the entire portion of the fox's chakra, and there is no fox to pull back on his chakra whenever he goes into KM/BM.
Not a true BM though
But, there is one thing you'd notice. Minato doesn't have an actual bijuu inside himself, he only has an unrestricted access to 50% of the most powerful bijuu's power. Therefore, minato cannot truly enter BM, but he can enter an Advanced KCM (super saiyan 1.5). His powers in KCM are much greater than naruto's KCM (more chakra = more power as we've seen with naruto going 1 tail, and jin and kin going 4 tail V2), but are a bit lower than naruto's BM, due to the simple fact that there isn't a fox to collect chakra, or help him break out of jutsu. Would naruto be able to use TBB and all that yada? Yes, he should. It's just collecting the right quantities of the blue and black chakra balls. But, Would he be able to break genjutsu? No. Would he have an automatic Defence cloak( Seen when kyuubi would automatically defend naruto before he ever acheived KM/BM)? No.
Final Note
It's possible that this is what's going on because jin and kin were able to enter V2 with absolutely 0 of the kyuubi's will. All they had was a small portion of it's chakra. But, What I'm saying, Is that minato has that, but at a grander level. A level so big that he can surpass V2, and KCM, and enter an advanced KCM.