First, re the question in the title: the negative isn't implicit, it is, as user10429 suspects, in the final /so/ (it is also implicit in the /yume/, of course, since this is only used in negative sentences).
But if it is final /so/, why is the verb /tamae/ instead of the expected /tamai/? There are a couple of possible explanations:
- The example in the dictionary is incorrect; it is not from real usage, and the person who wrote it didn't know how to use final /so/ properly
- The example in the dictionary represents some form of real usage, but that real usage (say, combination of final /so/ with the imperative form of the verb) was idiosyncratic to a particular time/place (say, early 20th-C pseudoclassical literary Japanese) and has been forgotten now
- The example in the dictionary is completely normal in terms of morphology; it is in fact the ren'yokei of /tamaeru/
Explanation (1) basically allows us to treat this example as an aberration. We don't need to revise our understanding of how final /so/ works if this is true. The difficulty is that we can never find positive evidence that explanation (1) is true -- only ever-increasing amounts of evidence failing to falsify it. (This is a standard philosophy of science issue, of course...)
Explanation (2) would be the most interesting. We could prove it by finding other examples of this usage pattern, and this would expand our knowledge of how final /so/ works. The example raised in comments, /osanago ni ataetamae so/ is a possible avenue for this. I'll explain it below.
Explanation (3) seems very unlikely because, as broccoli forest's comment quoted above notes, /tamaeru/ is (to simplify) a "humble-izer" and it would be strange to include it in an imperative construction like this.
Now let's consider /osanago ni ataetamae so/. First of all, it should be noted that this is the title of a translation by Okada Saburo of a short story by Max and Alex Fischer, original title "On ne devrait faire aux enfants", translated in English as "Unto these little ones" in the collection Estelle. The title refers to a song by Massenat, lyrics Boyer, that plays a role in the story. Here's the first stanza:
On ne devrait faire aux enfants
Nulle peine, même légère.
Ils sont si doux, ces innocents,
Suspendus au sein de leur mère!
For reference, here's the translation included in the English short story:
Unto these little ones, one should not mete
A grief, however slight,
Cradled upon a mother's breast,
They are so innocent, so sweet.
Now if you look again at /osanago ni ataetamae so/ you will see that it is in a 5/7 poetic form:
Osanago ni/ ataetamae so...
Clearly, /osanago ni ataetamae so/ is both title of the story and first few lines of the song, just as in the original.
But reconsider that part of the song: It's not in the imperative mood. Not "Don't mete a grief, however slight...", but "One should not mete a grief, however slight..."
I am going to go out on a limb here and advance the hypothesis that Okada intentionally used /-tamae so/ instead of /-tamai so/ because he wanted to reproduce that not-quite-an-imperative feeling. Like, maybe his /-tamae/ is the ren'yokei of some causative of /-tamau/, i.e. "Do not allow a grief to be meted..." (although the standard way to do this would be to add the causative bit to the main verb and leave /tamau/ alone, e.g. /ik.ase.tamae/ "let/cause to go"). Maybe he's saying to hell with it and going full izenkei. I am not aware of anything like this actually being a thing in pseudo-classical Japanese in the early 20th century, but I can certainly believe that a translator might experiment with such things even if it didn't stick.
If this is true, it would correspond to explanation (2), and it might make the example sentence acceptable with a slightly indirect meaning: "One should absolutely not breathe a word of this to anyone." The way to prove this hypothesis would be to find other examples of Okada and ideally his peers doing similar things. Even just tracking down Okada's translation and seeing how the line works in context would be a start.
Anyway, this is all pretty abstract stuff... I am very curious about it now, but I think as a basic answer, it would probably be best to summarize:
- The negativity is in the /so/ and implicit in the /yume/
- Setting aside the issue of whether the example is an error or not, one would certainly expect to see it written /-tamai so/ instead of /-tamae so/.