Just as Mahayana sutras in general, we can say tantras being the words of the Buddha except when stated otherwise (just like there are sutras taught by Shakyamuni's immediate disciples, bodhisattvas and other buddhas).
Early tantric scriptures (called sutras in Chinese) begin with the usual form:
Sūtra of the Buddha-Crown Superb Victory Dhāraṇī:
"Thus I have heard: At one time the Bhagavān was staying in the Anāthapiṇḍika Garden of Jetavana Park in the city kingdom of Śrāvastī, together with a group of 8,000 great bhikṣus."
Buddha Pronounces the Mahāyāna Sūtra of the Holy Infinite-Life Resolute Radiance King Tathāgata Dhāraṇī:
"Thus I have heard: At one time the World-Honored One was dwelling in the Anāthapiṇḍika Garden of Jetavana Park in the city kingdom of Śrāvastī, together with a group of 1,250 great bhikṣus."
Then in later texts we see moving from a common setting into a meditative world. See how the Vairocanabhisambodhi Sutra (also called a tantra in Tibetan Buddhism) begins:
"Thus have I heard. At one time the Bhagavān (Lord) was residing in the vast adamantine palace of the Dharma realm empowered by Tathāgatas, in which all the vajradharas had all assembled; the great pavilion [comparable to] the king of jewels, born of the Tathāgata’s faith-and-understanding, play, and supernatural transformations, was lofty, without a center or perimeter, and variously adorned with great and wondrous jewel-kings, and the body of a bodhisattva formed a lion throne."
The Tattvasamgraha Sutra (tantra) beings:
"Thus have I heard, once, the Bhagavat who is endowed with the thunderbolt empowered pledge and distinguished kinds of knowledge of all the Tathagatas; who has received the Dharma Kingdom initiation of the three worlds and the jeweled crown of all the Tathagatas; who is the Lord of great yoga and the all-knowing knowledge of all the Tathagatas; who has realized the equality of all mudras of all the Tathagatas and by every action has fulfilled all desires in all worlds of living beings without exception; who is the great, compassionate Vairocana, forever existing in the three periods of time and who is every body, speech and mind thunderbolt, the Tathagata, dwelt in the palace of the Lord of the Akanistha heaven bedecked with great gems, hung with variously shaped bells, and adorned with crescent moons, laced silk tassels with precious gems, flower wreaths and colored banners that swayed in the breeze, and which was inhabited, praised and extolled by all Tathagatas."
In the latest tantras we see even more "abstract" settings. The Hevajra Tantra:
"Thus have I heard: At one time Bhagavan dwelt in the wombs of the Vajra Lady which are the Body, Speech and Mind of all the Buddhas."
The Guhyagarbha Tantra:
"Thus at the time of this explanation, the Tathagata, genuinely perfect buddha and transcendent lord, was endowed with great rapture which is the identity of the indestructible body, speech and mind of all the tathagatas of the ten directions and four times. This is the nature in which all of them without exception, none excepted and omitting none at all, are indivisible, without distinction or difference. In the abode of Akanistha, without extremes or centre, on the radiant wheel of pristine cognitions that is the limitless ground, there is his celestial palace, blazing forth with jewels of pristine cognition, completely uninterrupted throughout the ten directions of space, fashioned as a square because it is vast in measureless enlightened attributes, and adorned with projecting bays of precious gems which are the superior pristine cognition."
"However, the (commonly cited) words I have heard are not uttered on this occasion because there is no dichotomy between self and others. The words have heard indicate that there is a difference between the teacher and the retinue, whereas during the compilation of this (tantra), the teacher himself appears as the Lord of Secrets (Vairapani) and explains in this world at the present time the very teaching which he previously gave in Akanistha."
The Kulayaraja Tantra:
"At a time this sermon was taught in the realm No-Below (Akanishtha) [where] Reality is [like] the sky, and the dimension of Reality itself (dharmadhatu) [like] the vastness [of the sky]. There is the place where the Mind itself (sems nyid) exists.
In the untainted mansion of pristine awareness [the All-Creating Sovereign's] own being (rang bzhin), Her actuating essence (ngo bo), Her compassion and pristine awareness became manifest as [various] retinues in the following way:..."
"There is no such thing as the real mind. Ridding yourself of delusion: that's the real mind."
(Sheng-yen: Getting the Buddha Mind, p 73)
"Neither cultivation nor seated meditation — this is the pure Chan of Tathagata."
(Mazu Daoyi, X1321p3b23; tr. Jinhua Jia)
“Don’t rashly seek the true Buddha;
True Buddha can’t be found.
Does marvelous nature and spirit
Need tempering or refinement?
Mind is this mind carefree;
This face, the face at birth."
(Nanyue Mingzan: Enjoying the Way, tr. Jeff Shore; T2076p461b24-26)