Am I in a rebound relationship?

Soooo... I’m curious to hear unbiased opinions (don’t want to ask my friends). I’m not sure if I am a rebound. I suspect that I could be but there’s also signs that I’m not, so I just want to hear your input and/or stories.

Signs that I am:

1. He got out of a five year relationship only five months ago (but I did too with my ex).

2. He’s moving quickly with me.

3. He is still bitter about his ex (she cheated).

Signs that I’m not:

1. She has tried getting back with him since he’s talked to me, and he told her no. He’s shown me all of their texts and gave me his phone PW (which I don’t need but he did anyways).

2. He just bought a house near me. His ex and him used to live in a different state, so she’s actually not here.

3. He introduced me to his parents and all of his friends know of me, but we haven’t met. He’s met all of my friends. Just not my parents.

My gut tells me he genuinely cares for me, but I don’t want the logical side of me to just slip right out the window. I want to know if I’m probably a rebound