Addition/subtraction work out the same regardless of how you order the operations. If you do subtraction last you start with the original:

9-1+3

and you are adding 3 to the result of (9-1). Since you are trying to perform it before the (9-1) operation is carried out, you can add 3 to the 9:

12-1 = 11

or you can add three to the -1 and get:

9+2 = 11

You only end up with 9-4 if you were subtracting 3 rather than adding three. It all becomes more obvious if you read the original as:

9 + (-1) + 3