According to that PDF and Vissuddhimagga, it's the end of the second tetrad of Anapanasati one enters first jhana, but actually this is not correct.
But, why this is not correct?
The document „skill in some task that one is doing _part 2_.pdf“ is inline with the Kayagata-sati sutta and the Anapanasati sutta.
But, why this is according to the reality as mentioned?
"Breathing in long, he discerns, 'I am breathing in long'; or breathing out long, he discerns, 'I am breathing out long.' Or breathing in short, he discerns, 'I am breathing in short'; or breathing out short, he discerns, 'I am breathing out short.' He trains himself, 'I will breathe in sensitive to the entire body.' He trains himself, 'I will breathe out sensitive to the entire body.' He trains himself, 'I will breathe in calming bodily fabrication.' He trains himself, 'I will breathe out calming bodily fabrication.' And as he remains thus heedful, ardent, & resolute, any memories & resolves related to the household life are abandoned, and with their abandoning his mind gathers & settles inwardly, grows unified & centered. This is how a monk develops mindfulness immersed in the body.
1) Mastery in entering the first Jhāna when one wants to.
2) Mastery in remaining in the first Jhāna for as long as one has determined.
3) Mastery in emerging from the first Jhāna at the determined time.
4) Mastery in adverting one’s attention to the factors of the first Jhāna after one has emerged from it.
5) Mastery in reviewing the factors of the first Jhāna.
Adverting and reviewing both occur in the same mind-door thought-process (manodvāra-vīthi). Adverting is performed by the mind-door adverting consciousness (manodvārā-vajjana), which in this case takes as its object one of the five Jhāna factors such as applied thought. Reviewing is performed by the four, five, six, or seven reviewing impulsion consciousnesses that occur immediately after the mind-door adverting consciousness, and which have the same object.
After that, to attain the (e.g. ānāpāna) second Jhāna, one reflects on the disadvantages of the first Jhāna and the advantages of the second Jhāna: the one has the two gross factors of initial and sustained application, which the other does not have. And determining to remove the two grosser factors, one concentrates on the (e.g. ānāpāna) paṭibhāga·nimitta again, to enter into Jhāna. Then one emerges from that Jhāna, and if one sees only three Jhāna factors (joy, happiness, and one-pointedness), it means one has successfully attained the (e.g. ānāpāna) second Jhāna. Then one develops the five masteries of that Jhāna.
In the same way, one removes the factor of joy to attain the third Jhāna, which has only happiness and one-pointedness. And one removes the factor of happiness to attain the fourth Jhāna, which has only one-pointedness and equanimity. One develops the five masteries for all the Jhānas.
1) Skill in adverting the mind to Absorption,
2) Skill in entering Absorption,
3) Skill in maintaining Absorption,
4) Skill in emerging from Absorption,
5) Skill in reviewing Absorption.
There is also no "counterpart sign" defined in those suttas, because the "counterpart sign" defined in those suttas through the rūpa.
The first aggregate is form/body (rūpa) (based on the image of corporeality, so imaged (rendered), being figurativeness (symbolic character)). Rūpa literally means picture or image because it is the object of eye-consciousness (cakkhuviññāna). Common translations of rūpa include form and body (shell). Every one of us has a body. If the body is short, you say, “I am short.” If the body is beautiful you say, “I am beautiful.” If the body is sick, you say, “I am sick.” So you can see how easily we associate the body with the ‘self.’
Finally we come to what is known as Mastery of the Jhāna (vasī). Vasī means experience, proficiency, skill in some task that one is doing. A man possessed of vasī is endowed with absolute mastery over something.
Literally the word vasī means “one who has power,” which here implies one who has power over his actions, who can do what he wants to do, as can a powerful man. He is able to act with proficiency, speed, and skill, unhindered by anything, and succeeding as he wishes. Power in practising samādhi is the result of skill in practice. The more skilful one is, the more power one acquires. Therefore the meaning of vasī here is precisely “one who has power because he has skill in means.” Such a person has skill in relation to Jhāna in five ways.
One develops the five masteries for all the Jhānas.
In vipassanā meditation, it is to meditate vipassanā
Related topic: What does it mean _Meditation - Duration vs Quality_