How do the spheres with recorded prophecies appear in the Department of Mysteries?

Related: How do you listen to a prophecy without smashing it in Harry Potter?

How do the spheres with recorded prophecies appear in the Department of Mysteries?

• Does one automaticlaly get generated, when the prophecy is spoken?


• Does one get magically generated when someone tells DoM@MoM about a prophecy, with the exact prophecy?


• Does one simply record what a witness to a prophecy said?

In specific examples, would Trelawney's second prophecy (to Harry Potter) be recorded in DoM sphere when she spoke to Harry? Or only after Dumbledore informed them? And if Dumbledore didn't inform them it wouldn't be recorded there at all?