The founders or HK were of course Buddhist and so they used many Buddhist terms in naming things poetically .So they would know the story of this particular arhat,and being that the set has many tiger claw techniques this name would be very appropriate.
Taming the tiger would have the meaning of overcoming the wild inclinations of the mind that is the cause of the emotional afflictions.I have seen animals represented this way in Buddhism very often.Fer instanz pig-ignoranc snake-anger rooster-pride.In Tibetan Buddhism they talk about the mind being like a distracted monkey.
The tiger would have the added conotation of the aspect of the mind that is very vicious and dangerous.