Did you have the same issue before replacing the digitizer? I suspect that replacement digitizer is defective, try another known working digitizer to confirm.
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If issue persists, then you need someone with micro-soldering experience to fix as this is board related.
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One thing I want to point out that the Mini/Mini 2 replacement digitizers are notorious for ghost touching (iPad activates itself erratically), make sure you cover the bottom strip near home button with Kapton or any ESD tape.
Did you have the same issue before replacing the digitizer? I suspect that replacement digitizer is defective, try another known working digitizer to confirm.