Does this card's "place an opponent's Digimon under another opponent's Digimon's Digimon" inherited effect also place the Digivolution card owned by the opponent's Digimon being placed under the Digivolution card?

No. If a Digimon is placed in the digivolved source of another Digimon, the digivolved card it had will be trashed.

Astral Snatcher rulings (BT11-109)

1 official ruling from Bandai, last ruled Sep 22, 2022. Straight answers to how this card actually resolves.

Effect: [Main] You may place up to 3 Digimon cards with the [Bagra Army] trait from your trash under 1 of your Digimon as its bottom digivolution cards or under 1 of your Tamers. Then, if you have a Digimon or Tamer with the [Bagra Army] trait in play, place 1 of your opponent's Digimon under 1 of your opponent's other Digimon as its bottom digivolution card.
Security effect: [Security] Activate this card's [Main] effects.

Official Q&A

Does this card's "place an opponent's Digimon under another opponent's Digimon's Digimon" inherited effect also place the Digivolution card owned by the opponent's Digimon being placed under the Digivolution card?
No. If a Digimon is placed in the digivolved source of another Digimon, the digivolved card it had will be trashed.
Ruled Sep 22, 2022

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Questions and answers are Bandai's official rulings, collected and translated by the DigimonCardGame Wiki community and reused here under CC BY-SA. Card names and card text are © their respective publishers; Combalo is not affiliated with Bandai.

Astral Snatcher rulings (BT11-109)

1 official ruling from Bandai, last ruled Sep 22, 2022. Straight answers to how this card actually resolves.

Effect: [Main] You may place up to 3 Digimon cards with the [Bagra Army] trait from your trash under 1 of your Digimon as its bottom digivolution cards or under 1 of your Tamers. Then, if you have a Digimon or Tamer with the [Bagra Army] trait in play, place 1 of your opponent's Digimon under 1 of your opponent's other Digimon as its bottom digivolution card.
Security effect: [Security] Activate this card's [Main] effects.

Official Q&A

Does this card's "place an opponent's Digimon under another opponent's Digimon's Digimon" inherited effect also place the Digivolution card owned by the opponent's Digimon being placed under the Digivolution card?
No. If a Digimon is placed in the digivolved source of another Digimon, the digivolved card it had will be trashed.
Ruled Sep 22, 2022

Got a line that uses Astral Snatcher? Map it in the builder and share it with a link.