Why does post-increment work on wrapper classes

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It’s perfectly safe to use across platforms. The behavior is specified in §15.4.2 of the Java Language Specification (emphasis added):

The result of the postfix expression must be a variable of a type that is convertible (§5.1.8) to a numeric type, or a compile-time error occurs.

The type of the postfix increment expression is the type of the variable. The result of the postfix increment expression is not a variable, but a value.

At run-time, if evaluation of the operand expression completes abruptly, then the postfix increment expression completes abruptly for the same reason and no incrementation occurs. Otherwise, the value 1 is added to the value of the variable and the sum is stored back into the variable. Before the addition, binary numeric promotion (§5.6.2) is performed on the value 1 and the value of the variable. If necessary, the sum is narrowed by a narrowing primitive conversion (§5.1.3) and/or subjected to boxing conversion (§5.1.7) to the type of the variable before it is stored. The value of the postfix increment expression is the value of the variable before the new value is stored.

EDIT Here’s a more accurate equivalent of what’s going on in your example code:

Integer x = 0;
int temp = x.intValue();
x = temp + 1; // autoboxing!
System.out.println(temp + ", ");
System.out.println(x.intValue());

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