There are two main situations in which you could call for an initiative roll:
An enemy makes a hostile action
In the situation you described I'm not sure that drawing a sword would call for this. Instead, tell the players what he does and see how they react. If they say "I shoot him!", then you roll. If they say "I attempt diplomacy to calm the situation" then you don't.
- The enemy says something obviously threatening (e.g. "Prepare to die!" or "Guards, seize them!")
- The enemy goes to move (e.g. to flee, take cover, grab an item, charge, etc.)
- The enemy makes an attack (this may be a surprise round if you think it appropriate)
The PC makes a hostile action
Similar to above, this is anything for which the enemy would not just stand by and do nothing.
Here are some scenarios which might make this clear
Casandra is confronting a rival in a dark alley. It is not yet clear if there will be bloodshed or merely threats and a parting of ways.
- Casandra runs her hand through her hair (no initiative roll).
- Casandra runs her hand through her hair and flings a shuriken which was disguised as a hair clip (surprise round, followed by initiative roll).
- Casandra says "If I see you in my territory again I'll cut your throat." (intimidation roll, but no initiative).
- Casandra flees (initiative roll if her rival wishes to pursue).
- The rival draws a dagger (initiative roll depending on how Casandra reacts, no surprise round).