Brahma, Vishnu, Rudra, Ishwara, and SadaShiva are called Panchabrahmans. Kashmiri Shaivism too with the addition of Anashirta Shiva in the above five deities list calls them Karana Devas. Sri Abhinavagupta is an authority on matters regarding Kashmiri Shaivism. I'm here quoting his text Tantrasara in the below passages:
- Lord Vishnu among Six Karana Devas:
Brahma, Vishnu, Rudra, Isha, Sadashiva, and Anashritashiva are the six Karana devas (causal deities) which are directly linked with causality itself. Lord Vishnu being one of the Karana Deva automatically presides over various aspects of life and consciousness.
ब्रह्म-विष्णु-रुद्रेश-सदाशिवानाश्रिताख्यं कारणषट्कम् (Tantrasara chapter 6)
Brahma, Vishnu, Rudra, Isha, Sadasiva, and Anasritasiva are called as six causal agents
- Lord Vishnu presides over youth phase:
Our life can be divided into various phases like childhood, youth, old age, death, rebirth, and liberation. These six Karana Devas are Adhipati over these phases:
बाल्य-यौवन-वार्धक-निधन-पुनर्भव-मुक्त्यधिपतय एते। (Tantrasara chapter 6)
They are the superintending deities of childhood, youth, old age, death, rebirth, and liberation.
- Lord Vishnu presides over Throat during Prana:
During breathing out (which corresponds with Prana), these six causal deities appear over various places of the body starting from the heart to the Dwadashanta (12 fingers above head) and among these areas, Vishnu appears in the throat area:
एवं यथा प्राणे कालोदय:, तथा अपानेऽपि हृदयात् मूलपीङ्गपर्यन्तम्। यथा च हृत्कण्ठङ्ग-तालु-ललाट-रन्ध्र-द्वादशान्तेषु ब्रह्म-विष्णु-रुद्रेश-सदाशिवानाश्रिताख्यं कारणषट्कम्, तथैव अपानेऽपि हृत्कन्दानन्द-संकोच-विकास-द्वादशान्तेषु, बाल्य-यौवन-वार्धक-निधन-पुनर्भव-मुक्त्यधिपतय एते। (Tantrasara chapter 6)
Just as the emergence of time occurs in the form of prana, in the same way, it occurs even in apana, which proceeds from the heart to the end of muladhara. As the six causal agents. that is, Brahma, Vishnu, Rudra, Isha, Sadasiva, and Anasritasiva, who appear in the heart, throat, palate, forehead, randhra, and in the 'end of twelve' (dvadasanta), operate in the upper region. in the same way in apana, these deities operate from heart to generative organ, causing it to contract and expand, and in the "end of twelve' (dvadasanta). They are the superintending deities of childhood, youth, old age, death, rebirth, and liberation. (Tantrasara chapter 6)
- Lord Vishnu presides over the dreaming phase:
Four states of consciousness which are Jagrat, Swapna, Sushupti, and Turiya are popularly talked about in Vedanta. In Vedas also these four states in the form of four padas of Omkara correspond to Brahma, Vishnu, Rudra, and Ishwara (Atharvashika Upanishad). In Kashmiri Shaivism, the states of consciousness are Five, and the fifth is Turiyatita. These five are called 'Avasthas' and the sixth one is called 'Swabhavadasha' which is called Anashrita. Lord Vishnu presides over Swapna Avastha (dreaming phase):
तत्र च पञ्च अवस्था जाग्रदाद्या:, षष्ठी च अनुत्तरा नाम स्वभावदशा अनुसंधेया, इति षोढा न्यासो भवति। तत्र कारणानां ब्रह्मविष्णुरुद्रेशसदाशिवशक्तिरुपाणां प्रत्येकम् अधिष्ठानात् षडिवंशत्तत्त्वकलापस्य लौकिकतत्त्वोत्तीर्णस्य भैरवभट्टारकभेदवृत्तेर्न्यासे पूर्णत्वात् भैरवीभावः तेन एतत् अनवकाशम्। (Tantrasara chapter 13)
There are five states beginning with waking, etc., but the sixth is called Anuttara, the 'innate state' (svabhava dasha), which is to be conceived as uniting all. Therefore, placement (nyasa) should be sixfold. In these six Brahma, Vishnu, Rudra, Ishwara, Sadasiva, and Sakti, the causal deities, are abiding steadily in the host of thirty-six tattvas, separately in each. By the application of nyasa, one attains the fullness of Lord Bhairava, who transcends the phenomenal principles. In this way,
the state of Bhairava becomes manifest.
- Lord Vishnu as among Trinity:
Brahma, Vishnu, and Rudra are considered as presiding over creation, protection, and destruction generally in Hinduism itself. Sri Abhinavagupta too calls this triad Mayagarbhadhikari (who presides over the realm of Maya):
परमेश्वरेच्छाप्रेरितमायागर्भाधिकारीयरुद्रविष्णुब्रह्मा-दिद्वारेण। (Tantrasara chapter 11)
(For those desiring bhoga) descent of grace occurs by MayaGarbhadhikari (Presiding deities of the realm of Maya): Rudra, Vishnu, and Brahma who are impelled by the will of Parameswara.
Regarding incarnations of Lord Vishnu, as he is already one among the Karana devas it is just a simple task to take incarnations considering even Yogis can incarnate. Incarnations like Rama and Krishna historically took place in various phases of time as per Kashmiri Shaivism also. Actually, Lord Rama himself comes in the Guru Parampara of Kashmiri Shaivism. Similarly, Abhinavagupta himself has written a commentary on Bhagavad Gita which are teachings given by Lord Krishna. However the things like 'Lord Rama did this in this phase of life, 'Lord Krishna fought with this King' are not found in any major scriptures (Agama Shastras) of Kashmiri Shaivism as far as I know. Kashmiri Shaivism generally completely focuses on Yogic aspects only.