In my opinion what you are describing is way too fast. If someone did that when dating me, I would run.
But I'm not part of your situation, so my opinion doesn't matter. What matters is that it works for the two of you. You are fine with it, so that's covered. So my only advice would be maybe check with him if he is comfortable with it. Or be prepared to deal with the consequences if he isn't.
There are many versions between the original and the TMBG version and after. My personal favorite