The word avivesa signifies that the Lord appeared within the mind of Vasudeva. There was no need for a discharge of semen. That is the opinion of Sripada Sridhara Svami and Srila Visvanatha Cakravarti Thakura

Expressions researched:
"The word āviveśa signifies that the Lord appeared within the mind of Vasudeva. There was no need for a discharge of semen. That is the opinion of Śrīpāda Śrīdhara Svāmī and Śrīla Viśvanātha Cakravartī Ṭhākura"

Srimad-Bhagavatam

SB Canto 10.1 to 10.13

The Lord is already there within the mind, and consequently it is not astonishing for Him to appear as if born from a devotee's body. The word āviveśa signifies that the Lord appeared within the mind of Vasudeva. There was no need for a discharge of semen. That is the opinion of Śrīpāda Śrīdhara Svāmī and Śrīla Viśvanātha Cakravartī Ṭhākura.

SB 10.2.16, Translation and Purport

Thus the Supreme Personality of Godhead, who is the Supersoul of all living entities and who vanquishes all the fear of His devotees, entered the mind of Vasudeva in full opulence.

The word viśvātmā refers to one who is situated in everyone's heart (īśvaraḥ sarva-bhūtānāṁ hṛd-deśe 'rjuna tiṣṭhati (BG 18.61)). Another meaning of viśvātmā is "the only lovable object for everyone." Because of forgetfulness of this object, people are suffering in this material world, but if one fortunately revives his old consciousness of loving Kṛṣṇa and connects with Viśvātmā, one becomes perfect. The Lord is described in the Third Canto (SB 3.2.15) as follows: parāvareśo mahad-aṁśa-yukto hy ajo 'pi jāto bhagavān. Although unborn, the Lord, the master of everything, appears like a born child by entering the mind of a devotee. The Lord is already there within the mind, and consequently it is not astonishing for Him to appear as if born from a devotee's body. The word āviveśa signifies that the Lord appeared within the mind of Vasudeva. There was no need for a discharge of semen. That is the opinion of Śrīpāda Śrīdhara Svāmī and Śrīla Viśvanātha Cakravartī Ṭhākura. In the Vaiṣṇava-toṣaṇī, Śrīla Sanātana Gosvāmī says that consciousness was awakened within the mind of Vasudeva. Śrīla Vīrarāghava Ācārya also says that Vasudeva was one of the demigods and that within his mind the Supreme Personality of Godhead appeared as an awakening of consciousness.