It sounded fantastical to me as well. However, looking into it, if Cicero's reporting is wrong, it probably isn't wrong by a lot.
"Magi" was the name used for followers of Zoroastrainisim, which was the state religion in Persia at the time. It isn't anymore of course, but the religion itself is still very much alive and kicking. Modern Parsis* in fact do hold a very similar funerary practice, although using carrion birds rather than dogs.
Parsi funerals begin in a way familiar to many faiths: prayers are
chanted and mourners pay last respects.
But that's where the similarities end, says Khojeste Mistree, head of
the Zoroastrian Studies Institute in Mumbai.
"We have an unusual method of disposal of the dead. The Parsi corpse
is exposed to the rays of the sun, and the corpse is consumed or
devoured by birds of prey — vultures, kites and crows," Mistree says.
For Zoroastrians, burying or cremating the dead is seen as polluting
nature. So for centuries, the Parsis in Mumbai have relied on vultures
to do the work — that is, until the entire population of vultures in
the city vanished.
If I may speculate a bit, I know a lot of central Asian peoples have historically practiced exposure excarnation (as did a lot of the native peoples of North America). Zoroastrianism is thought to have evolved directly from Indo-Aryan religious practices at a time they were essentially fresh off the steppe (2nd Millenium BC), so it isn't entirely without precedent.
All modern practitioners across Asia seem to prefer to put the body on a high place so that its specifically birds that do the work. So its tempting to gig Cicero there. However, the structures Zoroastrians build for this purpose appear to have been developed long after Cicero, and Herodotus reported both birds and dogs used by Zoroastrians for this purpose as well.
* - As a famous example, Freddie Mercury's family was Parsi, and his funeral was officiated by a Zoroastrian priest. However his remains were cremated, not excarnated.