I doubt the Raft was created in response to the Sokovia Accords. They had a fully functioning floating supermax prison that clearly wasn't built overnight. If I had to guess, it had been built over time, maybe in response to the Incident in New York city or, at least, Ultron. Given that the FBI was involved in Scott Lang's case, my guess is superpowered crime has Federal jurisdiction, so it would be the Feds claiming jurisdiction.
As for Due Process and all that, I don't disagree. I took Costa's comment to be a bit hyperbolic, but we obviously never found out. It is true that both Hawkeye and Ant-Man received plea deals, so that would suggest a normal trial apparatus, but they were both in a privileged position as quasi-Avengers. They had people to vouch for them. But I wouldn't trust Costa's comments as 100% accurate.