If a merged creature with a coin counter on it dies or is put into exile, then with Athreos you return all its components "to the battlefield under your control" (to the extent they're cards still in their owners' graveyards or in exile, as the case may be). The components will enter the battlefield as separate permanents rather than being merged. (In particular, Snapdax's "Whenever this creature mutates..." ability won't trigger this way.)
Here, the effect of Athreos's last ability "can find the new object that a merged permanent becomes as it leaves the battlefield, [so] it finds all" of those components; if "that effect causes actions to be taken upon those [components], the same actions are taken upon each of them", to the extent possible (C.R. 723.3c, 723.3, 400.7h, 400.2, 609.3). (Note in particular that a token component of the permanent will have ceased to exist in the meantime [C.R. 111.8]).
Both cards get returned to the battlefield (but not merged).
721.3. If a merged permanent leaves the battlefield, one permanent leaves the battlefield and each of the individual components are put into the appropriate zone.
721.3c If an effect can find the new object that a merged permanent becomes as it leaves the battlefield, it finds all of those objects. (See rule 400.7.) If that effect causes actions to be taken upon those objects, the same actions are taken upon each of them.
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Why bother with mere rulings when so many answers can be found in the Rules?
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Here, the effect of Athreos's last ability "can find the new object that a merged permanent becomes as it leaves the battlefield, [so] it finds all" of those components; if "that effect causes actions to be taken upon those [components], the same actions are taken upon each of them", to the extent possible (C.R. 723.3c, 723.3, 400.7h, 400.2, 609.3). (Note in particular that a token component of the permanent will have ceased to exist in the meantime [C.R. 111.8]).
See also this thread and this thread.
EDIT (Sep. 4): Edit rule citations.
Both cards get returned to the battlefield (but not merged).