Surprisingly, when you perform operations on bytes the computations will be done using int values, with the bytes implicitly cast to (int) first. This is true for shorts as well, and similarly floats are up-converted to double when doing floating-point arithmetic.
The second snippet is equivalent to:
byte someVar;
someVar = (int) someVar - 3;
Because of this you must cast the result back to (byte) to get the compiler to accept the assignment.
someVar = (byte) (someVar - 3);