The Buddha's teachings are different from what Ajita Kesakambali taught.
The Buddha realized this (from MN 19):
"When the mind was thus concentrated, purified, bright, unblemished,
rid of defilement, pliant, malleable, steady, & attained to
imperturbability, I directed it to the knowledge of recollecting my
past lives. I recollected my manifold past lives, i.e., one birth,
two... five, ten... fifty, a hundred, a thousand, a hundred thousand,
many eons of cosmic contraction, many eons of cosmic expansion, many
eons of cosmic contraction & expansion: 'There I had such a name,
belonged to such a clan, had such an appearance. Such was my food,
such my experience of pleasure & pain, such the end of my life.
Passing away from that state, I re-arose there. There too I had such a
name, belonged to such a clan, had such an appearance. Such was my
food, such my experience of pleasure & pain, such the end of my life.
Passing away from that state, I re-arose here.' Thus I remembered my
manifold past lives in their modes & details. .....
"When the mind was thus concentrated, purified, bright, unblemished,
rid of defilement, pliant, malleable, steady, & attained to
imperturbability, I directed it to the knowledge of the passing away &
reappearance of beings. I saw — by means of the divine eye, purified &
surpassing the human — beings passing away & re-appearing, and I
discerned how they are inferior & superior, beautiful & ugly,
fortunate & unfortunate in accordance with their kamma: 'These beings
— who were endowed with bad conduct of body, speech & mind, who
reviled the Noble Ones, held wrong views and undertook actions under
the influence of wrong views — with the break-up of the body, after
death, have re-appeared in the plane of deprivation, the bad
destination, the lower realms, in hell. But these beings — who were
endowed with good conduct of body, speech, & mind, who did not revile
the Noble Ones, who held right views and undertook actions under the
influence of right views — with the break-up of the body, after death,
have re-appeared in the good destinations, in the heavenly world.'
Thus — by means of the divine eye, purified & surpassing the human — I
saw beings passing away & re-appearing, and I discerned how they are
inferior & superior, beautiful & ugly, fortunate & unfortunate in
accordance with their kamma.
The Buddha taught his followers to reflect in this way (from AN 5.57):
“This noble disciple reflects thus: ‘I am not the only one who is the
owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s
origin, kamma as one’s relative, kamma as one’s resort; who will be
the heir of whatever kamma, good or bad, that one does. All beings
that come and go, that pass away and undergo rebirth, are owners of
their kamma, heirs of their kamma; all have kamma as their origin,
kamma as their relative, kamma as their resort; all will be heirs of
whatever kamma, good or bad, that they do.’ As he often reflects on
this theme, the path is generated. He pursues this path, develops it,
and cultivates it. As he does so, the fetters are entirely abandoned
and the underlying tendencies are uprooted.
From SN 12.19:
“Bhikkhus, for the fool, hindered by ignorance and fettered by
craving, this body has originated. For the fool that ignorance has not
been abandoned and that craving has not been utterly destroyed. For
what reason? Because the fool has not lived the holy life for the
complete destruction of suffering. Therefore, with the breakup of the
body, the fool fares on to another body. Faring on to another body, he
is not freed from birth, aging, and death; not freed from sorrow,
lamentation, pain, displeasure, and despair; not freed from suffering,
I say.
From SN 44.9:
“And, Master Gotama, when a being has laid down this body but has not
yet been reborn in another body, what does Master Gotama declare to be
its fuel on that occasion?”
“When, Vaccha, a being has laid down this body but has not yet been
reborn in another body, I declare that it is fuelled by craving. For
on that occasion craving is its fuel.”
Also, please note that the term "kāya" has been used in the sense of physical body for example in SN 22.56 (although I know that it can be used to mean group or collection, when combined with other things):
eye, ear, nose, tongue, body, and mind consciousness.
cakkhuviññāṇaṃ, sotaviññāṇaṃ,ghānaviññāṇaṃ, jivhāviññāṇaṃ, kāyaviññāṇaṃ, manoviññāṇaṃ
Pali words for body apart from "kāya" has been used in this context, for example "sarira" in Dhammapada 400:
Akkodhanam vatavantam
silavantam anussadam
dantam antimasariram1
tamaham brumi brahmanam
Verse 400: Him I call a brahmana, who is free from anger, who
practises austerity, who is virtuous and free from craving, who is
controlled in his senses and for whom this body (i.e., existence) is
the very last.
Footnote 1. antimasariram: lit., one who has the last body. This is
his last body because he will not be reborn; he is an arahat.
From SN 15.3:
"This is the greater: the tears you have shed while transmigrating &
wandering this long, long time — crying & weeping from being joined
with what is displeasing, being separated from what is pleasing — not
the water in the four great oceans.
"Long have you (repeatedly) experienced the death of a mother. The
tears you have shed over the death of a mother while transmigrating &
wandering this long, long time — crying & weeping from being joined
with what is displeasing, being separated from what is pleasing — are
greater than the water in the four great oceans.
"Long have you (repeatedly) experienced the death of a father... the
death of a brother... the death of a sister... the death of a son...
the death of a daughter... loss with regard to relatives... loss with
regard to wealth... loss with regard to disease. The tears you have
shed over loss with regard to disease while transmigrating & wandering
this long, long time — crying & weeping from being joined with what is
displeasing, being separated from what is pleasing — are greater than
the water in the four great oceans.
"Why is that? From an inconstruable beginning comes transmigration. A
beginning point is not evident, though beings hindered by ignorance
and fettered by craving are transmigrating & wandering on. Long have
you thus experienced stress, experienced pain, experienced loss,
swelling the cemeteries — enough to become disenchanted with all
fabricated things, enough to become dispassionate, enough to be
released."
Also, please note that since some people do not accept the Digha Nikaya as genuine teachings of the Buddha (please see this question), I have quoted from all the other nikayas instead. Dhammapada is part of KN.