Skirting around debates about what counts as democracy and using it in the sense of the times, I think a key distinction here is about power relations within states Vs those between them.

Athens tended to back democratic factions over oligarchic ones and this meant many of the Delian league cities were democracies like Athens itself - some joined Athens after Athens supported democrats taking over.

However, over time, Athens' actions towards her allies became more 'tyrannical'. Thucydides certainly takes that view in his history of the Peloponnesian War, having Pericles frankly tell the Athenian assembly that they are tyrants over what were once their allies (and that having become so they have no choice but to continue in this vein)

The tyrannical nature of the relationship is mainly

• Forcing some members to join and refusing to let others leave

• Encouraging other members to pay cash rather than provide troops which meant that Athens was the one with the navy and others became more dependent [contrast here with Rome whose confederate allies provided men not money]

• Taking a cut of league money to pay for public works in Athens when it was meant for common use