As youngman and knotsciott indicated, the tile should be done first for the reasons both posters above indicated. Often the firebox surround is only three pieces of stone, a head and two legs, which have been pre-cut before the tile man even picks them up. They are also heavy and expensive. The tile man needs room around the outside of the stone to set it.
I often used a beaded scrible molding nailed to the edge of the mantel legs and head panel to return to the stone around the firebox. You just have to plan on how to handle the detail where it meets the plinth (or base and base cap wrap) at the base of the pilasters.
Good luck.
Jimc