Calling a method on a new object in Java without parentheses: order of operations violation?

This is because of how the grammar of Java language is defined. Precedence of operators comes into play just when the same lexical sequence could be parsed in two different ways but this is not the case.

Why?

Because the allocation is defined in:

Primary: 
  ...
  new Creator

while method call is defined in:

Selector:
  . Identifier [Arguments]
  ...

and both are used here:

Expression3: 
  ...
  Primary { Selector } { PostfixOp }

so what happens is that

new myClass().myFunction();

is parsed as

         Expression
             |
             |
    ---------+--------
    |                |
    |                |
  Primary        Selector
    |                |
    |                |
 ---+---            ...
 |     |
new   Creator 

So there is no choice according to priority because the Primary is reduced before. Mind that for the special situation like

new OuterClass.InnerClass()

the class name is actually parsed before the new operator and there are rules to handle that case indeed. Check the grammar if you like to see them.