In most cases, in all cases with me, I always carve and tool first then dye.
Reason being when you carve, or cut into, the leather you open a new layer of undyed leather. This is almost always undesirable as its difficult to match the color.
This does not apply to pre dyed leather obviously.
EDIT: Tandem posting with Paul, always uncomfortable.
Quote for the week: Some cause happiness wherever they go; others whenever they go. Oscar Wilde.
Second quote because I wont replace the first: Craftsmanship cant be replaced by efficiency. William.