Understand The Eternals of Sirius and similar situatios

I don't understand why you can play The Eternals of Sirius being with a pool of 4.

I always thought that at the end of any window you have to check your pool to see if you are ousted.
So I thought that in the "pay the cost" window you would play 4 pool and before reaching "apply the effect" window you would be ousted before getting the 5 pool.

So "pay the cost" and "apply the effect" are all in the same window? Or there are specific windows to check your pool to see if you are ousted and not at the end of each window?

Thanks


Name: The Eternals of Sirius
[LotN:U, POD:DTC]
Cardtype: Master
Cost: 4 pool
Gain 5 pool if you control a ready Minister, or add 5 blood to a Minister with capacity 9 or more in your uncontrolled region.
Artist: Alexander Dunnigan