My inquiry to AquaBounty Technologies, regarding the construction of their transgenic Salmon, was responded to very quickly by both the media relations staff and the Director of Research, John Buchanan. According to Mr. Buchanan, standard microinjection techniques were used to inject DNA from the Chinook Salmon into eggs of the Atlantic Salmon. Only the single fish gene and an associated promoter region, were transferred. This means nothing you wouldn't ordinarily consume if you ate a Chinook Salmon (i.e. typical vectors used for other types of genetic research, from viruses or bacteria) have been inserted into the Atlantic species.
Microinjection is a method that has been proven effective for inserting new DNA into animals, but whether or not the new DNA is taken up into the chromosomes of the egg, is left to chance. Other methods, like those that require a retrovirus, may be more efficient but they do introduce more health and safety issues.
I can still understand a concern for the ecosystem if these fish are released into the wild, but this certainly doesn't appear to be a threat to human health in terms of consumption of foreign material.