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A couple of things:

int i,j,tmp;

can be formatted better:

int i, j, tmp;

and actually isn't even necessary, as is explained later.

int j;
for (j = 0; j < size; j++)
{
    std::cout << array[j] << std::endl;
}

C++ conventions have braces on the same line as the statement:

int j;
for (j = 0; j < size; j++) {
    std::cout << array[j] << std::endl;
}

In fact, the first line can be merged into the loop:

for (int j = 0; j < size; j++) {
    std::cout << array[j] << std::endl;
}

j = i;
while (j > 0 && arr[j - 1] > arr[j]) {
    tmp = arr[j];
    arr[j] = arr[j - 1];
    arr[j - 1] = tmp;
    j--;
}

can be a for loop, as explained:

    j = i; // Initialization
    while (j > 0 && arr[j - 1] > arr[j]) { // Condition
        tmp = arr[j];
        arr[j] = arr[j - 1];
        arr[j - 1] = tmp;
        j--; // Decrement
    }

which turns into:

for (j = i; j > 0 && arr[j - 1] > arr[j]; j--) {
    tmp = arr[j];
    arr[j] = arr[j - 1];
    arr[j - 1] = tmp;
}

Now, why is the first line not necessary, and even discouraged?

Well, because you should declare variable right where you need them, and not before:

void insertion_sort(int arr[], int length)
{
    for (int i = 1; i < length; i++) {
        for (int j = i; j > 0 && arr[j - 1] > arr[j]; j--) {
            int tmp = arr[j];
            arr[j] = arr[j - 1];
            arr[j - 1] = tmp;
        }
    }
}