Notice how these sikkhati steps you quoted specifically are found at the conclusion of the anapanasati instruction.
This is very consistent with the proximate causation mechanism presented in the SN12.23.
“I say, bhikkhus, that the knowledge of destruction in regard to destruction has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for the knowledge of destruction? It should be said: liberation.
“I say, bhikkhus, that liberation too has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for liberation? It should be said: dispassion.
“I say, bhikkhus, that dispassion too has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for dispassion? It should be said: revulsion.
“I say, bhikkhus, that revulsion too has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for revulsion? It should be said: the knowledge and vision of things as they really are.
“I say, bhikkhus, that the knowledge and vision of things as they really are too has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for the knowledge and vision of things as they really are? It should be said: concentration.
“I say, bhikkhus, that concentration too has a proximate cause; it does not lack a proximate cause. And what is the proximate cause for concentration? It should be said: happiness.
(…)
The way I make sense of it is that as the practice gains consistency, it becomes more likely that all the proximate causes required for the happines
samadhi
insight threshold to be reached and eventually surpassed.
It is important as well that one keeps in mind that what one’s training here is about experiencing, witnessing these things - not to cause or eventuate them. All in all, AN10.2 and AN11.2 tells us above all the process is impersonal, natural and does not require intention to occur.
It is similar to what happens when cooking rice. You need to make sure to have a source of heat, a pot, rice and water in front of you (and in the right set up!). Then you need to sit and watch, witness / experience, the cooking process until the rice is cooked. Then, only then you can taste cooked rice, and say all the nice things you can say about it! 