4 official rulings from Bandai. Straight answers to how this card actually resolves.

Does this card's <Start Your Turn> effect apply even if my opponent only has 1 Digimon with no digivolution cards and the rest of their Digimon have digivolution cards?
Yes, it does.
Does this card's <Start Your Turn> effect apply if my opponent has a Digimon with no digivolution cards in their breeding area?
No, it doesn't check Digimon in the breeding area.
Does this card's <Start Your Turn> effect apply when my opponent doesn't have any Digimon in their battle area?
No, it doesn't. Your opponent has to have a Digimon in their battle area for it to activate.
When my blue Digimon attacks, can I suspend this Tamer even if my opponent has no Digimon in the battle area?
Yes, it is a "Do to effect. As such, it follows the rules detailed in the Detailed Rules. (Found in Effect Resolution/Related Information#Costs)
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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.