Is Zakat obligatory on money saved in an Islamic bank if the returns are spent on basic living necessities and the current salary is not enough to cover these necessities?

Perhaps the speaker means that if the return is spent before a year has passed, then there is no zakat (definition) on it; this is correct, because one of the conditions for zakat to be obligatory is the passing of a full Hijri year. As for the principal amount, zakat is obligatory on it at the end of every Hijri year if it reaches the nisab (definition). It is permissible for a woman to pay the zakat of her wealth to her poor husband who does not have enough to sustain himself and those whose basic needs he is obliged to provide for, even if he will spend it on her, provided that she gives him ownership of the zakat money.