Interstellar, after Cooper entered the five-dimensional space, why did he and Murphy leave their marks at that time?

See if my understanding is correct: this is divided into several time and space.

Before he was ready to go to heaven, when his daughter was a little girl, he left the sign "Don't go" in Morse code, leaving no other signs.

When his girl grows up, she remembers the signs in the house and then goes back to her room. At this time, two different spaces are connected together. By leaving a "Don't Go" sign, Cooper knew that the previous information was left by herself, and then she reacted to convey the information and left the theoretical knowledge she saw in the black hole.

It is also possible that Cooper did not have knowledge before he entered the black hole. Maybe he left a message when the little girl was young, but they didn't understand it at that time. So he doesn't know who left the message.

I don't know what to say, but it makes sense.