duymazlıktan gelmek = to pretend not to have heard
The person actually heard you but s/he is pretending that s/he didn't hear you, s/he is ignoring the person who is talking. The reason can be anything, fair or unfair.
Examples:
Your example: Bu sözleri duymazlıktan geldi. = S/he pretended not to have heard my words.
- Ona söylediğim halde beni duymazlıktan geldi. (Even though I told him, he pretended not to have heard me.)
- Haberi beğenmediği için duymazlıktan geliyor. (He is pretending not to have heard for he didn't like the news.)
* Also;
görmezlikten gelmek = to pretend not to see
anlamazlıktan gelmek = to pretend not to understand