You are right. It is easy to understand what is meant, but it is not quite correctly expressed. As Hot Licks says, we can easily understand that it must mean:-
... all three (tested) negative.
A literalist might say that this apparently means that all but three of the people tested were negative, which is not quite right. To understand the sentence in the way obviously intended, however, we have to start with a passive:-
...686 people have been tested,...
and then mentally wrench the verb tested round into the active. This is surely at best clumsy. We are, moreover, in doing so, using a special locution for cases where, if people were-tested-and-their-tests-came-out negative, we can shorten the whole thing down to tested negative. It is not hard to find an alternative that avoids this.
So far, 686 people have been tested, with negative results for all but three.
If we understand the original sentence, does it matter? I think it does, but, based on teh pre-eminence of usage, perhaps it does not. That is an argument for another question.