From the Dogma Clarifications section at the back of my Echoes rulebook:
Execute all non-demand dogma effects (slightly different wording in 1st/2nd edition base sets) refers only to the dogma effects of the card in question. It does not allow you to execute echo effects. You do not share effects, but some effects (Rocketry, Hot Air Balloon, etc) may impact other players.
Again, assuming that's what this rules question is about.