In MN 86 (quoted below), we find the lay bandit Angulimala cognizant of the psychic power displayed by the Buddha.
Then Aṅgulimāla donned his sword and shield, fastened his bow and
arrows, and followed behind the Buddha. But the Buddha used his
psychic power to will that Aṅgulimāla could not catch up with him no
matter how hard he tried, even though the Buddha kept walking at a
normal speed.
Then Aṅgulimāla thought, “It’s incredible, it’s amazing! Previously,
even when I’ve chased a speeding elephant, horse, chariot or deer,
I’ve always caught up with them. But I can’t catch up with this
ascetic no matter how hard I try, even though he’s walking at a normal
speed.”
In the Vinaya chapter Cammakkhandhaka (Pli Tv Kd 5) quoted below, we find the example of the Buddha asking a monk to perform wonders of psychic power for eighty thousand villagers to see.
Then those eighty thousand village overseers approached the Lord;
having approached, having greeted the Lord, they sat down at a
respectful distance. Then those eighty thousand village overseers paid
respect only to the venerable Sāgata, not likewise to the Lord. Then
the Lord, knowing by reasoning of mind the minds of those eighty
thousand village overseers, addressed the venerable Sāgata, saying:
“Well then, do you, Sāgata, abundantly show a state of further-men, a
wonder of psychic power.”
“Very well, Lord,” and the venerable Sagata, having answered the Lord
in assent, having risen above the ground, paced up and down in the
air, in the atmosphere, and he stood, and he sat down, and he lay
down, and he smoked and he blazed, and then he vanished.
Then the venerable Sagata, having shown in the air, in the atmosphere,
various states of further-men and wonders of psychic power, having
inclined his head towards the Lord’s feet, spoke thus to the Lord:
“Lord, the Lord is my teacher, I am a disciple; Lord, the Lord is my
teacher, I am a disciple”. Then those eighty thousand village
overseers, saying: “Indeed it is marvellous, indeed, it is wonderful,
that even a disciple can be of such great psychic power, of such great
might. What must the teacher be?” paid respect only to the Lord, not
likewise to the venerable Sagata.
The story in the commentary to Dhp 124 (quoted below) has a demonstration of psychic power by the Buddha to Kukkutamitta and his family, but it's not clear if they were cognizant of it.
When the hunter came, he saw no animal in the trap; he saw the
footprint and surmised that someone must have come before him and let
cut the animal. So, when he saw the Buddha under the shade of the
bush, he took him for the man who had freed the animal from his trap
and flew into a rage. He took out his bow and arrow to shoot at the
Buddha, but as he drew his bow, he became immobilized and remained
fixed in that position like a statue. His sons followed and found
their father; they also saw the Buddha at some distance and thought he
must be the enemy of their father. All of them took out their bows and
arrows to shoot at the Buddha, but they also became immobilized and
remained fixed in their respective postures. When the hunter and his
sons failed to return, the hunter's wife followed them into the
forest, with her seven daughters-in-law. Seeing her husband and all
her sons with their arrows aimed at the Buddha, she raised both her
hands and shout: "Do not kill my father."
When her husband heard her words, he thought, "This must be my
father-in-law", and her sons thought, "This must be our grandfather";
and thoughts of loving-kindness came into them. Then the lady said to
them, ''Put away your bows and arrows and pay obeisance to my father".
The Buddha realized that, by this time, the minds of the hunter and
his son; had softened and so he willed that they should be able to
move and to put away their bows and arrows. After putting away their
bows and arrows, they paid obeisance to the Buddha and the Buddha
expounded the Dhamma to them. In the end, the hunter, his seven sons
and seven daughters-in-law, all fifteen of them, attained Sotapatti
Fruition.
In the Vinaya chapter Mahākhandhaka (Pli Tv Kd 1) quoted below, the Buddha used his psychic power to temporarily hide Yasa from his father, both of whom were laypersons at the time. However, it appears that they were not cognizant of the fact.
The Lord saw the (great) merchant, the householder, coming in the
distance; seeing him, it occurred to the Lord: “Suppose I were to
perform such a psychic wonder that the (great) merchant, the
householder, sitting here, should not see Yasa the young man of
family, sitting here?” Then the Lord performed such a psychic wonder.
Then the (great) merchant, the householder, approached the Lord;
having approached he spoke thus to the Lord: “Lord has the Lord not
seen Yasa, the young man of family?”
“Well, householder, sit down. Perhaps, sitting here, you may see Yasa,
the young man of family, sitting here.”
