Cloudflare uses an 'Auto' TTL that resolves to a low value — commonly 300 seconds — and for records proxied through Cloudflare (the orange-cloud icon) the address visitors resolve is Cloudflare's edge, which updates almost immediately at the origin without waiting on a public DNS TTL at all. This is why changing a record in Cloudflare's dashboard usually shows up in seconds to a couple of minutes, far faster than a legacy registrar with a one-hour default.
The one time you still wait is the initial move to Cloudflare, when you change your domain's nameservers at your registrar to the pair Cloudflare assigns you. That delegation change is cached at the TLD level and can take up to 24 hours to complete worldwide, even though everything inside Cloudflare is ready instantly. Cloudflare emails you when it detects the domain is active; until then, some resolvers may still consult your old DNS host.
Because Cloudflare's TTLs are so short, a record you edit and then revert will also settle quickly, which makes it a forgiving place to experiment. If you proxy a record, remember that public DNS tools will show Cloudflare's IP ranges rather than your origin server's real address — that is by design, not a propagation error.