[Luminion Lancer]

The way I understood it, the original seal system that kept Kurama locked allowed tiny portions of his chakra to seep into Naruto's own reservoir, even when he wasn't drawing upon it, thus slowly expanding his supply.

Then it was revealed that the chakra that Kurama has is downright poisonous to anyone who doesn't have the body of a physical god and the potent chakra to filter it for use. That's when it was revealed that the Uzumaki are distant relatives to the Senju who themselves are descended of the Sage's Son with the strongest body. Naruto being able to withstand 4, 6 and even an 8-tailed transformation with little consequence is proof of that. It is even further driven home by Kushina, who not only lived (for a while at least) after Kurama was extracted but was also capable of casting a potent restraining jutsu afterwards.

The way I see it, this was kind of like taking a half-full bucket of water and sealing it into an airtight, impregnable safe, with only a small hose that periodically allowed for droplets of water to fall into the bucket inside from a nearby ocean. It wasn't much, but over time that bucket began to overflow and is currently filling the safe to the brim.