a real tiger in Calvin's personal reality

Correct!

Calvin sees Hobbes differently from everyone else. Each sees a different reality, and each person's reality is self-consistent. Watterson says he thinks that's how life works (and I agree, by the way): none of us sees the world in exactly the same way. He says he just draws that literally, in the strip.

And don't forget, in the strip itself, we see plenty of evidence that Hobbes is capable of hiding information from Calvin and doing both physical and mental labor to help Calvin out.