You can't. If the options were "eldonis, eldonas, eldonos" then all of them would work.
If they were "eldonis, eldoni, eldono", though, then only "eldonis" works grammatically -- not because it is past tense but because it is a finite verb. (At first, I had "eldonu" as an option but that would also work grammatically.)
If the question really was ambiguous, i.e. more than one of the options made sense - is there a way to report it? That sort of thing should hopefully get blocked somehow.
(Do you remember what the other options were?)
German for publisher (the person and the company) is Herausgeber, which literally translates to English as outgiver and to Esperanto as fordon(ad)isto or more idiomatically as eldon(ad)isto. But eldonisto only really makes sense for the person. For the company it makes more sense to conceive of it as a place, hence eldon(ad)ejo. Not using the optional part -ad (which signals that the action is done habitually) makes sense for brevity.
(German for publish is herausgeben. Much of the above is applicable to the verb as well. Note that herausgeben and Herausgeber are ambiguous and may mean edit and editor. This does not seem to be the case in Esperanto.)
I am not convinced it was a good idea to build the Esperanto word following this pattern. Unless you happen to be a German speaker it's not at all clear how to interpret this word. Theoretically, an eldonejo could also be a distribution point for food and other aids after a natural disaster - for example. In fact, even though I'm a German speaker I didn't immediately recognise this calque as such and had to use the hint.
I think your approach and mine are both reasonable ways of explaining a situation that is really quite a bit more complicated. The German preposition heraus should really be translated as something like eksteren, because it is used for movements from inside something to the outside. (Nominally in the direction of the speaker, who is outside. In contrast to hinaus, which is reserved to when the speaker is inside. But in practice, heraus, especially in its colloquial short form raus, is used more generally.) Lernu.net gave me for as its translation of heraus. This surprised me at first, but when you examine the ways these two prepositions are used in practice, this does actually make sense.
I would say that "eldonejo" is (or should be) "publishing house", and "eldonisto" is "a publisher". ("Eldonanto" would perhaps be used of someone who is not a publisher by profession, but is perhaps publishing something as a "one-off".)
eldonejo is a publisher in the sense of a "publishing house", that is, a place/company, that publishes works.
eldonanto is a publisher in the sense of a person, that publishes something.
They happen to translate to the same word in English, but in other languages, for example Bulgarian, there are separate words, like in Esperanto. This is just one of those cases where Esperanto is clearer than English.
This is ricidulos - I have been doing Esperanto for over a year now and every time, literaly every time I come accross this sentence, before reading the whole sentence, I translate "eldoni" as "a lighter". A special question for everybody here - who can tell me why I keep doing that? The correct answer will bring you 10 lingos ;)