"Once all assignments have been made, they take effect simultaneously."
"All required actions responding to a particular trigger are performed before any optional actions."
"When the Free Peoples player assigns one of his characters to skirmish a minion with the keyword "ambush
," the Shadow player who owns that minion may add
."
"
DESERT RUNNER 7 C 133
Clarification:
Southron. Ambush
.
When the Free Peoples player assigns this minion to a character and you have initiative, you may wound that character."
(Quotes from rulebook: assignment, action, ambush,
Desert Runner clarification.
Desert Sneak and
Desert Scout have the same clarification.)
You cannot assign in a particular order (unless via assignment actions). So all Southrons get assigned simultaneously, Chieftain action is required and takes place before all others (which are optional).