Purphoros will trigger for each Ornithopter that enters the battlefield at the same time as it, per 603.6a.
603.6a. Enters-the-battlefield abilities trigger when a permanent enters the battlefield. These are written, "When [this object] enters the battlefield, . . . " or "Whenever a [type] enters the battlefield, . . ." Each time an event puts one or more permanents onto the battlefield, all permanents on the battlefield (including the newcomers) are checked for any enters-the-battlefield triggers that match the event.
[emphasis mine]
So all the permanents, including Purphoros, are checked for any ETB triggers that match the event. Purphoros's ETB trigger therefore goes off, since creatures were put onto the battlefield. It will trigger 4 times (since it doesn't trigger for itself, the ability reading "Whenever another creature...").
All the permanents DO enter the battlefield at the same time; the order has no effect on triggering abilities, since triggers are essentially checked once all the permanents are on the battlefield.
Also, @Nighthawk: you're not "resolving" any of these creatures. You're resolving Protean Hulk's triggered ability. As part of the resolution of that ability, the Ornithopters and Purp enter the battlefield.