There aren’t any suttas that i am aware of that go into the specifics, but the Visuddhimagga discusses it in some details here:
[(5) THE DIVINE EYE—KNOWLEDGE OF PASSING AWAY AND
REAPPEARANCE OF BEINGS]
72. As to the explanation of the knowledge of passing away and reappearance
of beings, [here is the text: “He directs, he inclines, his mind to the knowledge of
the passing away and reappearance of beings. With the divine eye, which is
purified and surpasses the human, he sees beings passing away and
reappearing, inferior and superior, fair and ugly, happy or unhappy in their
destiny; he understands beings as faring according to their deeds: ‘These worthy
beings who were ill-conducted in body, speech and mind, revilers of Noble
Ones, wrong in their views, acquirers of kamma due to wrong view, have, on the
breakup of the body, after death, appeared in a state of loss, in an unhappy
destiny, in perdition in hell; but these worthy beings, who are well conducted in
body, speech and mind, not revilers of Noble Ones, right in their views, acquirers
of kamma due to right view, have, on the breakup of the body, after death, appeared
in a happy destiny, in the heavenly world.’ Thus with the divine eye, which is
purified and surpasses the human, he sees beings passing away and
reappearing, inferior and superior, fair and ugly, happy or unhappy in their
destiny; he understands beings as faring according to their deeds” (D I 82).
Herein,] to the knowledge of the passing away and reappearance: cutúpapátañáóáya=
cutiyá ca upapáte ca ñáóáya (resolution of compound); [the meaning is,] for the kind of knowledge by means of which beings’ passing away and reappearance
is known; for knowledge of the divine eye, is what is meant. He directs, he inclines
his mind: he both directs and inclines preliminary-work consciousness. He is
the bhikkhu who does the directing of his mind.
73. But as regards with the divine eye, etc., it is divine because of its similarity to
the divine; for deities have as divine eye the sensitivity that is produced by
kamma consisting in good conduct and is unimpeded by bile, phlegm, blood,
etc., and capable of receiving an object even though far off because it is liberated
from imperfections. And this eye, consisting in knowledge, which is produced
by the power of this bhikkhu’s energy in development, is similar to that, so it is
“divine” because it is similar to the divine. Also it is “divine” because it is
obtained by means of divine abiding, and because it has divine abiding as its
support. And it is “divine” because it greatly illuminates by discerning light.
And it is “divine” because it has a great range through seeing visible objects
that are behind walls, and so on. All that should be understood according to the
science of grammar. It is an eye in the sense of seeing. Also it is an eye since it is
like an eye in its performance of an eye’s function. It is purified since it is a cause
of purification of view, owing to seeing passing away and reappearance.
74. One who sees only passing away and not reappearance assumes the
annihilation view; and one who sees only reappearance and not passing away
assumes the view that a new being appears. But since one who sees both outstrips
that twofold [false] view, that vision of his is therefore a cause for purification of
view. And the Buddhas’ sons see both of these. Hence it was said above: [424] “It
is ‘purified’ since it is a cause of purification of view, owing to seeing passing
away and reappearance.”
75. It surpasses the human in the seeing of visible objects by surpassing the
human environment. Or it can be understood that it surpasses the human in
surpassing the human fleshly eye. With that divine eye, which is purified and
superhuman, he sees beings, he watches beings as men do with the fleshly eye.
76. Passing away and reappearing: he cannot see them with the divine eye actually
at the death moment of reappearance.17 But it is those who, being on the verge of
death, will die now that are intended as “passing away” and those who have
taken rebirth-linking and have just reappeared that are intended by “reappearing.” What is pointed out is that he sees them as such passing away
and reappearing.
77. Inferior: despised, disdained, looked down upon, scorned, on account of
birth, clan, wealth, etc., because of reaping the outcome of delusion. Superior: the
opposite of that because of reaping the outcome of non-delusion. Fair: having a
desirable, agreeable, pleasing appearance because of reaping the outcome of
non-hate. Ugly: having undesirable, disagreeable, unpleasing appearance
because of reaping the outcome of hate; unsightly, ill-favoured, is the meaning.
Happy in their destiny: gone to a happy destiny; or rich, very wealthy, because of
reaping the outcome of non-greed. Unhappy in their destiny: gone to an unhappy
destiny; or poor with little food and drink because of reaping the outcome of
greed…
Hope that helps.
Maybe it’s just my reading of the suttas, but the Buddha does seem to have had a wonderfully dry sense of humour.
Reminds me I really need to work on my meditation to escape all of this 
!