Is it the case that when I am reciting the Qur’an and someone speaks to me, I should continue or respond?

There is no harm in interrupting recitation to answer someone who speaks to you about an important matter. However, it is preferable to dedicate oneself entirely to recitation. If a Muslim greets you, or sneezes, or you hear the call to prayer (adhan), or your parent calls you, or an emergency occurs, there is no harm in interrupting. In fact, it is obligatory to return the greeting of peace and to respond to one's parents.