If the rest of the UK is expected to put it's interests after Northern Ireland's than that would ALSO be an example of the tail wagging the dog.
It's a metaphor used to describe a situation more than anything else.
Of course we should look after the interests of Northern Ireland, but in alignment of our own itnerests, not Ireland's.
Both the EU and Ireland can't keep throwing the "You guys decided to leave the EU, you sort it." line at us. The problem is really the EU itself, because it's a protectionalist trading block.