In Revenge of the Sith, it's a plot point that Obi-Wan and Yoda are changing the Jedi Temple beacon's message at the same time that Padme and Bail are learning about the formation of the Empire:
The PILOT pushes some buttons. MAS AMEDDA appears on screen.
MAS AMEDDA: Senator Organa . . . the Supreme Chancellor of the Republic requests your presence at a special session of Congress.
BAIL ORGANA: Tell the Chancellor I will be there.
MAS AMEDDA: Very well. He will be expecting you.
MAS AMEDDA's image disappears from the screen.
BAIL ORGANA: It could be a trap.
OBI-WAN: No, I don't think so. The Chancellor will not be able to control the thousands of star systems without keeping the Senate intact.
YODA: If a special session of Congress there is, easier for us to enter the Jedi Temple it will be.
Based on this exchange and the cuts seen in the film itself, the Emperor is declaring his intention to create the Empire to the Senate roughly concurrently with Obi-Wan and Yoda's trip to the Jedi Temple. Later, Rebels shows a holocron containing Obi-Wan's overwritten version of the Temple's warning message:
OBI-WAN: This is Master Obi-Wan Kenobi. I regret to report that both our Jedi Order and the Republic have fallen, with the dark shadow of the Empire rising to take their place. [...]
How did Obi-Wan know about the Empire if he was recording the message at the same time everyone else was finding out about it elsewhere?
EDIT: According to issue 2 of the Kanan: The Last Padawan comic, it looks like it is indeed the same message--that is, the one we see in Rebels is the same one recorded during the events of RotS.