I used to tap with my pointer finger and only tapping down on the string.

But I read/heard that you're suppose to use your middle finger and tap down on the string and slightly pull off or flick the string.

Which one is correct if not both?
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just tap how you feel like it, im not sure there is a correct way, i even use my pick sometimes
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If you use your middle finger you can still hold your pick. That's why they say that. And flicking or "pulling off" is essentially just that. It's just another pull off.
i use my index but if it hurts from tapping to much then i use my middle
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It doesn't matter which finger you use, so long as when you pull-off, you slightly flick your finger off in a downwards motion. Personally, I find that I get better control when tapping with my index finger because I can rest my thumb on the neck and use my palm to mute unwanted strings.
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pick tapping creates a trilling sound though.

That's because you're trilling with the pick, it only has a trilling sound if you're trilling with it, it doesn't automatically have a trilling sound.