With cylinders, it depends almost entirely on the external loading of the structure, in the absence of axial or radial loading on the thin walled cylinder, then hoop stress is the greatest.
And with hoop stress, the inside of the cylinder has the greatest stress. This is due to receiving the same total strain, but the outside having a greater circumference in which to distribute it over. So with the absence of axial or radial loading, a fracture in a cylinder should always begin on the inside of the cylinder.
However, a cycle frame isn't really exposed to pressure differentials, so the hoop stress should remain fairly constant.
Though, this same difference in circumference, is what increases the strain externally in axial and radial loading.
It is incorrect to say that a crack always starts on the inside, as with no increases in axial or radial loading, cracks will nearly always form internally. However, with axial and radial loading, if they go beyond the UTS before the hoop stresses reach it, then the crack will likely form on the outside.
However, the effect is negligible on something with wall thickness as little as they are on bicycles, any impact strong enough to fracture a well manufactured carbon tube, is likely to fracture completely through inside and outside.