Struggling to remember my AOP training, but ISTR that "Splash, Out" was optional, particulary as, on hearing "Splash, Over" you may be struggling with the controls as you got back into a position where you might spot the fall of shot.
The report of splash is used in both VP and Fire Orders.
If conducting an Arty Target Indication Mission on Battlegroup Net where the observer is a non Arty Foo the procedure is conducted using VP and splash will be sent to the FOO who will pass on to the actual observer the same report.
If conducting a Fire Mission on the Arty Net the observer may request report of splash at any stage in the adjustment or effect phase of the mission.
If the observer conducting the mission is an AOP then the report of splash is sent by the BCP by convention and is not required to be read back by the observer(also by convention) for the reasons stated by Cloudbuster as above. If memory serves......