Yes, hence why the rules refer to this type of attack as a random attack. It just avoids having to draw initiative twice or rolling a die.
I'm a little confused by this. I don't have the rulebook with me, so apologies in advance, I'm doing this from memory.
1. The encounter starts by revealing the card.
2. Initiative is dealt.
3. Everyone sets their action.
4. Initiative is revealed. (There's one(?) potential action card to be played here to change initiative.)
5. Pre-attack actions are called for (Edge out, other?).
6. Attacks are revealed, in initiative order.
7. Monster then attacks player #s as specified on the card.
...or, is does the monster attack after step two in the next round? (so the players still all only get one action, but don't know at that point if they will be targeted)?