Regardless of what seal he has now, he doesn't have the same seal as Naruto. However, the reason why Minato still has the Bijuu within him is because of plot most likely. Minato has gotten two pretty useless and bad power-ups since his awakening, Bijuu mode being one of them. What we know is that the Reaper Death Seal seals the user and its target into the belly of the reaper, then they both die. However, Minato didn't die as a following of the seal. That is most likely why Kurama was sealed within himself rather than the reaper. That is also why Orochimaru's arms, Tobirama and Hashirama's souls were sealed within the reaper. Kurama is bound to Minato's physical body, while the souls was sealed away inside of clones and ended up inside of the reaper. Orochimaru's arms also ended up within the reaper as they are not bound by Hiruzen's physical state as he died from the sealing. Causing the reaper to take both his soul and Orochimaru's arms.