i += Increment(ref i); is equivalent to
i = i + Increment(ref i);
The expression on the right hand side of the assignment is evaluated from left to right, so the next step is
i = 0 + Increment(ref i);
return i++ returns the current value of i (which is 0), then increments i
i = 0 + 0;
Before the assignment the value of i is 1 (incremented in the Increment method), but the assignment makes it 0 again.