No. 'You tiger' formal would be capitalised: "la Sua tigre" http://italian.about.com/library/fare/blfare132a.htm
both suo/sua are used for his and her, and if you put IL suo or LA sua, it means his or hers.
For knowing which one is used, it's pretty clear whithin the context (in exercices like this both possibilities would be correct, in real life you know what people are talking about so it's easier to get it)
My mistake was not in the pronoun but in the gender of the animal because of the article. I got "his tigress is sweet" as wrong and I really don't get it. If "tiger" is both male and female, shouldn't the article specify the gender? Il tigre = the tiger / La tigre = the tigress. Therefore "La sua tigre" = His/her tigress. What is wrong in my logic? Thanks :)