I am confused by the admonition of the Church on burial and against spreading ashes in light of the practice of dividing the remains of saints and scattering them throughout the world.

There are important differences between the practices. Relics usually involve small portions of the body, such as bone fragments to be reserved for veneration. Thus the entire body of a saint is not “scattered” throughout the world, or even scattered locally as with strewn ashes.
 
Secondly, the relic of the saint is retained for veneration as a kind of physical and visual memory, whereas scattered ashes are spread in order to disappear and return to the elements. And while some may find this meaningful, the result is that any physical reminder of the person is lost, quite different from a relic.
 
Thirdly, with a relic, the physical presence of a small portion of the body is treated with reverence, much as a gravesite would be, and prayers are often said in its presence in acknowledgment of the given saint. In the case of scattered ashes, neither the ashes nor the place of their dispersal receive the same kind of veneration, and may in fact be tread upon by human beings unaware of their presence, and by wild animals.
 
While it will be admitted that burial practices have some variance across cultures, the current practice of the Church, out of respect for ancient Christian practice and current sensibilities, is to insist that human remains of any sort be buried or entombed. The Order of Christian Funerals has this to say about the disposition of cremated bodies: The cremated remains should be buried in a grave or entombed in a mausoleum or columbarium [a cemetery vault designed for urns containing ashes of the dead]. The practice of scattering cremated remains on the sea, from the air, or on the ground, or keeping cremated remains in the home of a relative or friend of the deceased are not the reverent disposition that the Church requires.