JavaScript and Java have pretty much strict left-to-right evaluation rules for this expression. C does not (even in the version you provided that has the identity function intervening).
The ECMAScript spec I have (3rd Edition, which I'll admit is quite old – the current version can be found here: http://www.ecma-international.org/publications/files/ECMA-ST/Ecma-262.pdf) says that compound assignment operators are evaluated like so:
11.13.2 Compound Assignment ( op= )
The production AssignmentExpression : LeftHandSideExpression @ =
  AssignmentExpression, where@ represents one of the operators indicated
  above, is evaluated as follows:
- Evaluate LeftHandSideExpression.
- Call GetValue(Result(1)).
- Evaluate AssignmentExpression.
- Call GetValue(Result(3)).
- Apply operator @ to Result(2) and Result(4).
- Call PutValue(Result(1), Result(5)).
- Return Result(5)
You note that Java has the same behavior as JavaScript – I think its spec is more readable, so I'll post some snippets here (http://java.sun.com/docs/books/jls/third_edition/html/expressions.html#15.7):
15.7 Evaluation Order
The Java programming language guarantees that the operands of
  operators appear to be evaluated in a specific evaluation order,
  namely, from left to right.
It is recommended that code not rely crucially on this specification.
  Code is usually clearer when each expression contains at most one side
  effect, as its outermost operation, and when code does not depend on
  exactly which exception arises as a consequence of the left-to-right
  evaluation of expressions.
15.7.1 Evaluate Left-Hand Operand First The left-hand operand of a binary operator appears to be fully evaluated before any part of the
  right-hand operand is evaluated. For example, if the left-hand operand
  contains an assignment to a variable and the right-hand operand
  contains a reference to that same variable, then the value produced by
  the reference will reflect the fact that the assignment occurred
  first.
...
If the operator is a compound-assignment operator (§15.26.2), then
  evaluation of the left-hand operand includes both remembering the
  variable that the left-hand operand denotes and fetching and saving
  that variable's value for use in the implied combining operation.
On the other hand, in the not-undefined-behavior example where you provide an intermediate identity function:
x += id(x += 1);
while it's not undefined behavior (since the function call provides a sequence point), it's still unspecified behavior whether the leftmost x is evaluated before the function call or after.  So, while it's not 'anything goes' undefined behavior, the C compiler is still permitted to evaluate both x variables before calling the id() function, in which case the final value stored to the variable will be 1:
For example, if x == 0 to start, the evaluation could look like:
tmp = x;    // tmp == 0
x = tmp  +  id( x = tmp + 1)
// x == 1 at this point
or it could evaluate it like so:
tmp = id( x = x + 1);   // tmp == 1, x == 1
x = x + tmp;
// x == 2 at this point
Note that unspecified behavior is subtly different than undefined behavior, but it's still not desirable behavior.