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Should the spatial complexity of an insertion sort be O (N)?

This covers the "software algorithm" from https://stackoverflow.com/help/on-topic

This is from a class lecture slide enter image description here

Here is the insertion sort implementation we used

public static void insertionSort(int[] a) {
     for (int i = 1; i < a.length; i++) {
          int temp = a[i];
          int j = i;
          while (j >= 1 && a[j - 1] > temp) {
                a[j] = a[j - 1];
         }
         a[j] = temp;
     }
}

I would agree that the spatial complexity of the local variables will be O (1), because every time the size of the input file, i, j and temp will be processed only by the same local variable, each will occupy a block of memory.

However, I am confused by the spatial complexity of the array. http://www.cs.northwestern.edu/academics/courses/311/html/space-complexity.html had a similar example,

int sum(int a[], int n) {
    int r = 0;
    for (int i = 0; i < n; ++i) {
       r += a[i];
    }
    return r;
}

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