"B when (whenerver) A" means: "if A, then B".
"not-p is true whenever p is false"
means: "if p is false, then not-p is true", which is another way to state the Law of Exclude Middle.
Bivalence and Excluded Middle are obviously related, but they are not the same.
See Bivalence: Relationship to the law of the excluded middle:
The difference between the principle [of bivalence] and the law [of excluded middle] is important because there are logics which validate the law but which do not validate the principle. For example, the three-valued Logic of Paradox (LP) validates the law of excluded middle, but not the law of non-contradiction, ¬(P ∧ ¬P), and its intended semantics is not bivalent. In classical two-valued logic both the law of excluded middle and the law of non-contradiction hold.
Bivalence is a semantical principle: it states that the semantic has only two truth values.
Exclude middle is about the negation "opeartion".
We may have a logic with more than two truth values and we may have a logic without negation.
In classic logic, where we have a bivalent semantic and the negation sign, the two interact via the truth table.
The negation "swaps" the truth value:
p is TRUE iff not-p is FALSE,
and this is LEM.