Recursion confusion with multiple return

I'm still wrapping my mind around recursion, and I think I get basic ones like factorial. But I'd like further clarification when the return statement is a little more complex like on the following snippet:

/**
 * @param n >= 0
 * @return the nth Fibonacci number 
 */
public static int fibonacci(int n) {
    if (n == 0 || n == 1) {
        return 1; // base cases
    } else {
        return fibonacci(n-1) + fibonacci(n-2); // recursive step
    }
}

In the return statement, does the fibonacci(n-1) completely recur through, before going down the fibonacci(n-2) step (does that make sense)? If so, this seems very difficult to envision.