Basically, there are three waves of assignments, each of which has a different rule regarding how many minions can be assigned to a companion.
Assignment actions:
No companion may ever be assigned to more than one minion.
Free Peoples player assigns minions who were not assigned by assignment actions:
Each companion may be assigned to one minion (or may be left unassigned), and each companion who is defender +X may be assigned to a maximum of X additional minions. Note that any minions who were assigned during assignment actions count towards these limits.
Shadow player assigns minions who were not assigned by assignment actions or by the Free Peoples player:
Each companion may be assigned to an unlimited number of minions.
Note that defender bonuses only apply to the Free Peoples player's normal assignments, not to assignment actions or the Shadow player's assignments (where they'd be moot, anyway).