Correct on both accounts.
Initiative triggers on attacks. Recruitment into occupied cities count as attacks:
When you are attacking, destroy two units from the target troop before the beginning of the battle.
The controlled player can recruit units as normal. This will immediately trigger a battle (it will be an attack).
Recruitment scribe only triggers when making the recruiting action:
Recruiting Scribe wrote:
The Recruit action gives you 2 more units.