Is this true that it is a commonly agreed rule that $\forall x\in A:P(x) \wedge Q$ and $\forall x\in A:P(x) \Rightarrow Q$ should be interpreted correspondingly as $(\forall x\in A:P(x)) \wedge Q$ and $(\forall x\in A:P(x)) \Rightarrow Q$?
The question is about implied parentheses. Are the other interpretations $\forall x\in A:(P(x) \wedge Q)$ and $\forall x\in A:(P(x) \Rightarrow Q)$ common?
The reason that it is customary to "bind variables tightly" is to ensure we have clarity regarding the scope of a quantified variable. Absent any parentheses, the tightest of bounds applies.
To omit parentheses is sloppy, at best, but it happens (to the misfortune of those who have to mind-read with respect to the author's intention).