As for giving advance notice to the other three gods of the future, so they could protect Atabia's traverse and descent, and prevent others from taking the chance to ambush him, traversing to their own present world?
No way.
Time is essentially another dimension.
The other three really can't guard those unseen time channels.
The four Authorities, to be honest, are all a bit off in their own direction; each fights their own fight, plays their own game, and none can really do anything to the others.
If you do a Space Jump, how are the other three supposed to stop you?
You can only jump however you like, play by yourself, and the three of us can only watch—there's really nothing we can do to you.
You do Time Travel?
That's also you playing solo, and we still can't stop you.
On their own power, they can only traverse seven or eight seconds into the past, but since you already opened the channel, they really can crawl along that channel all the way to some distant present.
