While DNS caches can sometimes impact DNS updates, we rebuild the entire zone file when a DNS value is updated, and purge the previous cache. Even for customers, this should happen pretty quickly. We maintain a 5 minute TTL on all proxied records internally. So, this happens much faster than most other DNS services.
Yeah - that's a pretty standard way of doing things, and thats how DNS servers themselves will operate (mostly) when you make an update to a recordset.
Its not your cache that is the issue.
People have miss behaving caches, that do not always respect TTLs, some apps can cache the DNS response (I remember a Java issue where the initial value found was cached for the lifetime of the process!).
The TTL publicly is static and doesn't matter. The resolver you hit will just point to Cloudflare NS. Why we are faster, is because we point internally, and we don't have misconfigured TTLs or caching (I mean, things happen but it's not common). So once you update the global resolvers your visitors would hit to point to CF, their cache/TTL should never matter since we dictate where our internal DNS points the requested record.