This may be correct. When you work in Arkansas your employer will withhold AR income taxes. You will file as a nonresident in AR. If the AR withholding is not enough to cover the AR taxes you will owe AR. If you owe Arkansas review your state entries to make sure you are filing as a "Non-Resident". As a nonresident you should only pay taxes on income earned in Arkansas.
Since you are a Mississippi resident all of your income, regardless of where you worked, is taxable to Mississippi. This means the income made in Arkansas is taxable in Mississippi. Since you would not have had any MS withholding you have nothing to offset the MS tax due. You will get a credit for the taxes you pay to Arkansas so that will help some, but it is almost a given that you will owe Mississippi taxes.