What you read is correct. If the interaction is significant, interpreting either main effect, whether significant or not, is basically pointless (and misleading). The reason is that when $A$ and $B$ are involved in an interaction, the coefficient for $A$ is the effect of $A$ when $B=0$; in other words, the effect is conditional on the value of $B$, and is not a main effect. Similarly, the coefficient for $B$ is the effect of $B$ when $A=0$.
The fact that $A$ is significant merely means that $A$ has an effect when $B=0$. Similarly, the fact that $B$ is not significant merely means that $B$ doesn't have an effect when $A=0$, though it probably does have an effect for other values of $A$; this is precisely why the interaction is significant.
What you would need to do is look at simple slopes, which shows the significance of the $A$ effect as a function of the $B$ variable. You need to determine at which values of $B$ does $A$ have an effect, and vice-versa. Kris Preacher provides an online tool to decompose 2-way interactions in linear mixed models.