Why don't Java's +=, -=, *=, /= compound assignment operators require casting?

As always with these questions, the JLS holds the answer. In this case §15.26.2 Compound Assignment Operators. An extract:

A compound assignment expression of the form E1 op= E2 is equivalent to E1 = (T)((E1) op (E2)), where T is the type of E1, except that E1 is evaluated only once.

An example cited from §15.26.2

[...] the following code is correct:

short x = 3;
x += 4.6;

and results in x having the value 7 because it is equivalent to:

short x = 3;
x = (short)(x + 4.6);

In other words, your assumption is correct.

A good example of this casting is using *= or /=

byte b = 10;
b *= 5.7;
System.out.println(b); // prints 57

or

byte b = 100;
b /= 2.5;
System.out.println(b); // prints 40

or

char ch = '0';
ch *= 1.1;
System.out.println(ch); // prints '4'

or

char ch = 'A';
ch *= 1.5;
System.out.println(ch); // prints 'a'

Very good question. The Java Language specification confirms your suggestion.

For example, the following code is correct:

short x = 3;
x += 4.6;

and results in x having the value 7 because it is equivalent to:

short x = 3;
x = (short)(x + 4.6);