Same Source

The Heavenly Will and probably the rest of the world could not have imagined that when the Heavenly will has successfully been born, there were mortals, living beings inside Earth itself that could surpass it.

As for Chapter the Will of the Universe or the Will of the Omniverse, the name itself is very self-explanatory. 

Of course, these wills, this personification of the will themselves might not all themselves the Will of the Universe or the Will of the Omniverse

But that is how Hikigaya refers to them

Azief breakthrough disturb the natural order. Because he stands taller than the Heavenly Will. 

And not only the natural order of Earth but beyond it was also disturbed with each breakthrough. 

Probably it could no longer ignore it. Or maybe, only now, the Will of the Universe felt threatened

And so, the Will of the Universe descend down. 

And they are determined to wipe out Death Monarch from the face of the Universe.