Reverie starts at 903 , simultaneously as Wano started.
And reverie didn't go on weeks , it effectively removed Warlord systems and they went after them.
Blackbeard took the chance to go to Boa.
While shanks came to wano thinking he would came for Luffy.
Shanks in Wano
And BB at Amazon lily happened simultaneously, that's why shanks couldn't find Blackbeard.
They bounties were out even before he went to Boa.
There's no premises to say It went according to how you're stating it to be.