No, they're taking turns. They're on a clearly defined round-based system. If I recall correctly, they're still on the 6-second round system, but they can gain multiple actions in a single round.
No, they're not taking turns. Round is not turn.
Let me try to explain this simplest of distinctions.
Turn-based:
Combat starts.
Each character, the pcs and enemies, get their order of turn.
Character with first turn takes action.
Everyone else waits. No action.
Character with second turn takes action.
Everyone else waits. No action.
...
Character with the last turn takes action.
Everyone else waits. No action.
Everyone has finished taking their actions.
End of round.
Round 2 starts.
...
Real-time:
Combat starts.
Everyone starts taking actions.
Nobody waits for other characters to finish their actions.
Each action takes a set amount of time, called round. (3 seconds in these games)