Double apostille: when the stamp is needed both on the original and on the translation
"I was told the apostille is needed on the translation as well — is that even a thing?" Yes, and it is not exotic. Some states — certain authorities in Italy, Portugal, and a number of Latin American countries — do not recognise a translation made abroad unless the translation itself is legalised. The scheme is then: apostille on the original → notarised translation of the original together with the apostille → apostille on that notarised translation.
Why one apostille is not enough
An apostille confirms the authenticity of a signature and seal on a specific document for a state party to the Hague Convention. When a Russian translator and a Russian notary add their own signatures and seals to the file, a new official document is formally created — a notarial act performed in Russia. For the receiving country it too needs confirmation: otherwise it is unclear who this notary is, whether their licence is valid, and whether the named translator exists at all. The second apostille — on the notarised translation — closes that gap.
The key point is sequence. The original is apostilled first. Then it is translated together with the apostille stamp, because the apostille is part of the document and its text must appear in the translation. Then a notary certifies the translation, and it is that notarial act that receives the second apostille. Translate before apostilling the original and it all has to be redone: the translation will not contain the apostille.
How to tell whether you need a double apostille
The only reliable source is the written requirement of the receiving organisation. Marker phrases: "apostille on the translation", "legalizzazione della traduzione", "traduzione asseverata e apostillata", "legalización de la traducción", "apostille on the translation". If you see one of these, allow an extra 1–2 working days for the second apostille and warn the agency in advance: the translation needs to be bound from the outset in a format suitable for re-apostilling, rather than re-bound afterwards.
If, on the other hand, the receiving side simply asks for a "notarised translation with apostille" and nothing more, it almost always means one apostille on the original, with the translation certified by a notary. Do not add a second apostille "just in case": that is extra money and extra days, and there is always one specific set of actions that is actually required.