I find this unlikely, although I admit that it's a valid reading of the ability sans examples.
However, they as game designers should know not to use game terms in ambiguous circumstances. Adjacency bonuses always are cumulative; that is, if I have n adjacent tiles that satisfy the condition, then I should get n * bonus additional resources from adjacency. (Yes, it's not quite that with the minor/0.5 bonus.)
Why, then, would they turn it around and use it for just a single yield increase? 'Your Districts get +1 to their primary yield while adjacent to another District' is far clearer and avoids confusion of reserved game terms.