MAN THE CANNONS!

[Shurrikhan]

Why not both?

That would also be fine in normal as long as you bait each tornado away from the cannons. Having two people on the cannons at all times generally makes it trickier to use them (due to failure to bait and thereby blocking cannons with—might be showing by age here—rather painful DoT-afflicting ground effects) than a single cannonier. Ideally, if the mobility is there, it should be used, because there's no opportunity cost anyways (apart from one person's cast-time on the cannon).

[Sieben79]

Had to do Stone Vigil last time. As a healer it's hard to manage the cannons, if the tank is to far away and then one of the two tornados get stucked at the cannon I have to manage while the dragon also constantly interrupt me and damage the whole party or at least 2 of the DD. If shit goes this way then you should switch with one DD and do less damage at the boss (as a healer you can also do damage, it's just lesser and the fight will take a bit longer).

Under perfect circumstances let the healer handle the cannons but shit happens often.

[HaelseMikiro]

Ideally the healer will do it. With a smart party the tank will never be out of range even if the healer is standing at the cannons.
Sometimes you get a tank that's a ding-dong and they try to tank the boss right in the doorway between the 2 braziers, and that can cause lots of problems. The bosses whirlwinds target players and then travel in a straight line until it his a wall, and tanking in the doorway tends to put the party between the boss and the cannons, so whirlwinds go that way. Especially melees with rear positionals.
As a healer you can stand to the sides of the cannons to safely bait whirlwinds, and easily sprint when needed to fire a cannon. Although upcoming changes to Sprint in 4.0 put it on a 60 second cooldown, so there's that to think about T.T