It works as follows: When you sign up to enable direct deposit, FTX opens an account for you at Evolve. You can use that account number to have some or all of your paycheck direct-deposited. When you buy cryptocurrencies on FTX, that account is automatically debited. (This avoids the ACH transfer step if you were to purchase using your "regular" bank account.)
I may be missing something, but I'm pretty sure the deposited funds are FDIC insured, up until you use them for a purchase. But FTX isn't allowed to say that without mentioning the name of the actual bank (Evolve), and the FDIC thinks the "until you use them for a purchase" part of the preceding sentence is confusing.
I agree with the FDIC here, but I don't think FTX's statements were particularly nefarious. There's more nuance here than could fit into the tweet this C&D is about.
Edit to add: this is how FTX explains it when you enable this feature on their site (no mention of FDIC insurance, but if it's a regular checking account, the unspent funds in that account would be protected if either FTX or Evolve went bust): https://pifke.org/ftxdd.png