I see a couple options. Just keep it secret, or slowly reveal a little at a time. I have four wolf shirts, and I wear them a ton. My family knows I absolutely love wolves. I've even said a couple times that I feel like I have the power of a wolf inside me, and I compare myself to wolves sometime. And they have seen firsthand my ability to communicate with dogs.
Just start getting tiger themed whatever so it's obvious you love them, which no one thinks is weird. And start making the occasional comparison between yourself and tigers. And just slowly show a little more every now and then. Much safer than one day walking up to someone and saying "Oh, and I feel like I'm actually a tiger". Just slowly let them make the connect between you and tigers, and things should move forward.
Oh, and for now, no one knows I'm a therian, and only one of the six other people in the house know I'm a furry, so keeping it secret while you slowly introduce the connection is quite possible.