When I moved reddit from one datacenter to another, about 70% of the traffic shifted within the TTL. Another 20% moved within a week. Took till the end of a month after the change to get to about 98%

But after two months, about 1% was still going to the old server (I had set it up as a proxy for the cutover). Most of that traffic looked like crawlers that were written in things like Python or Ruby and had probably hard coded the IP or done something where it just didn't know what a TTL was.

So at that point I just shut down the old server.

You're probably right about API clients using better resolvers though. I was talking about consumer facing things where a lot of people would be on ISP DNS.