Not entirely true:
The attack automatically affects any target within
Reach of the initial target, and then one additional target
within Close range for each Effect rolled, starting with the
next closest target (at the gamemaster’s discretion if it is
not obvious).
First, EVERY target within Reach of the initial target will be hit even without rolling any Effects.
Then for each Effect rolled another target in the same zone, within Close range, will be hit, starting with the ones closest to the initial target.
Most Minions acting as a Mob are within Reach of each other. So a hit with the area quality that hits a Minion will get all other Minions in the same Mob even without any Effects rolled on the damage dice.
And those Minions within Reach get the full damage applied to each one, as Minions don’t get to make any kind of Reaction.
If there were Toughened or Nemesis NPCs within Reach or in Close Range when the Effects are applied, they get to make a Difficulty D2 Reaction to get out of the way of the area effect damage.
But Minions cannot, can never react - so a Mob of Minions getting hit for sufficient damage to take one out, will take out the whole Mob at once.
This is especially effective for Area effect Threaten Attacks - like Sorcerous Might or a Mighty Name, which tend to send whole mobs of Minions running away in fear, never to return.
You only use the propagation of damage on other members in a mob, when this is NOT caused by area effect damage. So a single melee attack on an initial Minion might kill this one right away and wound or even kill another one. This is the usual way, often still enough to kill off a whole mob of Minions, but only after applying the propagation rules.
Area effect damage will kill off Mobs of Minions without any problem - therefore: use more mobs of Minions, or split them into more smaller mobs instead of having only one or two 5-NPC-mobs, that raises the chances that at least one mob is still able to act after an area attack by the PCs.
ADD ON:
In the official Errata PDF things are described quite differently:
How do Area attacks (p.152) work with Mobs and Squads? (p.306)
As with a normal attack, an attack with the Area quality against a mob targets a single individual member of that mob to start with. Effects rolled with the Area trait allow additional targets to be hit, which can be other members of the mob. Between this and damage carrying over across a mob, Area attacks should be quite effective against mobs.
This Errata clarification seems to ignore that all targets within Reach of the primary target automatically get hit - no Effects necessary.
Apparently, this Errata and Clarification PDF needs some Errata and Clarifications, as this clarification given is in conflict with the actual rules text of the Area quality.