If your first card played is Darius Trifarian then you play a spell, does Darius immediately trigger before any player gets priority?

No. Darius does not trigger until the spell (your second card) has fully resolved — not when the spell is placed on the chain.

Per Rule 419.4.a, "when you play" triggers happen after the card resolves, not when it enters the chain. So the sequence is:

1. You play the spell — it goes on the chain.
2. Players pass priority; the spell resolves.
3. After resolution, Darius sees that the second card was played. His mandatory trigger goes on the chain.
4. Players get priority to respond to Darius's trigger.

If the spell is countered, it was never "played" (Rule 419.4.b), and Darius won't trigger at all. (FAQ #2630 covers this exact timing with Challenge — Darius's +2 always comes after the spell resolves.)