When the poison took effect, Alex let it do so because being poisoned and in pain was a good way to get the man to waste time and not attack him. Alex was fully intending on doing just that while, internally, he slowly got rid of the poison as well.
His Undying Body could likely help him survive even without that, but it would use so much energy, which Alex didn't want to waste. Why should he waste Qi to survive the poison when he could purge it from his body and gain Qi from it? It was a win-win situation.
So, while he partially dealt with the poison, he left just enough of it in his body that he could put on the effect of being poisoned.
Alex could tell that the man wasn't directly connected to the poison through his Creation, or else he would've realized.
