I agree with your translation, and agree that the translator has strayed. Traduttore, traditore.
But I don't think the appearance of "first" has to imply something heretical. It's really more a case of the adverb appearing at an unconventional spot in the sentence. All it means to me is the sequence of events: first the plan of salvation is fulfilled in Jesus Christ. Following which, the faithful are invited, etc.
Yes, I agree that is what the translator meant.