Is it incumbent upon a person to seek forgiveness from another if they said to him, "May Allah forgive you," in a simple situation?

The phrase "May Allah forgive you" (الله يسامحك) is originally a supplication for good and does not create any right for the person being supplicated for over the supplicant. However, it may be used to imply a shortcoming or wrongdoing, in which case it is understood as a disparagement and an offense to the person being addressed, similar to someone who says it while intending backbiting. If it is said with the intention of implying wrongdoing, then the one who said it must seek absolution and forgiveness from the person to whom it was said. Otherwise, it is a supplication for good.