After an unsuccessful run on this Assault, I'll post what I learned did work.
Capturing an Apkullu is very easy once you have a Hamsi in your inventory:
1. Stand in front of a "calm" Apkullu (ie. one that has not recently "run away" and is simply walking around).
2. If the Apkullu is able to be captured, the log will read "The Apkullu stares at you."
3. Target the Apkullu, and type /bow. The log should read "The Apkullu is wary of your presence."
4. Immediately target the Apkullu and type /welcome after the "wary" message. If you time it correctly, the log will read "The Apkullu seems to like you."
5. Immediately move directly behind the Apkullu and click it to give the Hamsi. If you were quick enough trading, you will successfully capture the Apkullu every time.
Guiding the Apkullu to the Prof is a different story... I couldn't figure that part out. I always seemed to scare him away no matter how close or far I followed.