I used to operate an anycast DNS service and we monitored it from probes all over the world. Sometimes a random ISP in USA/Europe would start sending queries to Japan and that could last for seconds to hours. I'm not sure how often it happens, but it will certainly be enough that it will cause broken connections for a few users.

I'm not sure how Cloudflare deals with it - potentially they could share the TCP connection data between datacenters when needed.

Or maybe it has something to do with their how edgy their setup is - if it's mostly intra-ISP cache servers being anycasted, the routing should be more stable.