Ships always have difficulties with anything over the horizon.
Assuming the DF-21D is deployed, in a hypothetical conflict that will involve a US carrier fleet, China will be under constant satellite watch long before that, and pay no mind to the usual anti-satellite weapon hype by the Chinese here, one test does not make a weapon, anyway, once a DF-21D is launched from anywhere inside mainland China, its flight will be calculated before it even reach mid-point and an SM-3 will have a solution for mid-phase interception. The fleet will be alerted and maneuvers planned to create as large a search area as possible for the warhead, assuming it survive the SM-3. At 30+ knts speed, in 15 min there will be at least a thousand square km to search.
But back to reality...The DF-21D have yet to have an open water test in clear weather. China have been under constant satellite surveillance since the Cold War. No ballistic missile launch can escape US. China cannot test the DF-21D over the east -- Japan and South Korea. Cannot test in the south because of Taiwan and the high traffic area of the South China Sea. That leave the little bit more open East China Sea and the test launch would be broadcast for Japan to know. The DF-21D have yet to test against the weather. And finally against man-made countermeasures.
All of these are unknown. The PLA can declare the weapon to be 'deployed' but it would be meaningless. Such a statement cannot guarantee successes or even a pK of 50%. In order to increase range, the DF-21D launches should be as near the coast as possible, but that would leave them vulnerable to preemptive attacks from US B-1s and B-2s. Moving them further back in land reduces their estimated threat range into the sea.