This is from the Dwarf FAQ
Q. May a Master Engineer with the Rune of Luck use
the rune to re-roll a to hit roll for a Bolt Thrower he is
acting as an Artillery Master for? Also, may a Master
Engineer with the Rune of Luck use the rune to re-roll
a to wound roll for a Bolt Thrower, Cannon, or Grudge
Thrower he is acting as an Artillery Master for?
A. No.
Here, despite the fact that one could reasonably assume that since his BS is being used, he is the one firing the machine. But, as this response shows, the bolt thrower shot does not count as one of his own missile attacks.
The situation is exactly the same with the imperial engineer.