Here is a link to a post with more info about nouns. https://forum.duolingo.com/comment/32745349 The confusing thing is that this post says "The noun class M/Wa applies to all people". However the tips for the People Skill says that it applies to "Most nouns referring to humans".
Anyway, wiktionary says "Daktari" is in the "ma" class. This would explain the use of Wako here, because as mentioned in the tips for the People Skill, "For the M- WA- noun class, the prefix w- is used for both singular AND plural possessive pronouns."