The first thing to do is to remember that if the character just declares a readied action, they'll be able to get a shot off at the first thing to pop into their field of vision anyway.
The DMs issue was that he wasnt prepared to explain to the PCs what was triggering the initiative check. Why ready an action to do something, when there is no information to go on as to why you need to?
Example (how not to do it from a DM perspective)
DM (noting hidden monsters in ambush): OK, as you walk through the forest... roll initiative!
Players (in unison): Huh? Why?
DM: You dont know why. Just roll.
Players: Ummm... OK (roll).
DM: OK Player 1, you go first and due to the Alert feat, you're not surprised. What do you do?
Player 1: What do I notice?
DM: (noting hidden monsters have yet to attack) Nothing. Nothing has changed from a few seconds ago.
Player 1: (
correctly refusing to meta-game) Oh... OK. Well I guess I keep doing what I was doing before you called for initiative.
I've seen DMs do exactly the above before.
It should be:
DM (noting hidden monsters in ambush): OK, as you walk through the forest, suddenly the whistle of arrows can be heard in the air, and you see movement from the trees all around you. A black fletched arrow thunks into a tree near the Wizard. You're all
surprised. Roll initiative!
Players: (Roll initiative).
DM: OK Player 1, you go first and due to the
Alert feat, you're not surprised. What do you do?
Player 1: Can I see these archers?
DM: (noting monsters are hidden) No, they're still currently hidden from you. You can take the Search action to try and locate them if you want?
Player 1: Nah screw that, I'll cast
Mirror Image, and leap for cover behind that tree 20' away.
The problem stems from the DMs lack of narration in example 1 to signify the transition from narrative time to combat time. If he used a different approach at the transition phase, his problems totally disappear.