After you file

It depends.  In general, you are correct that Alabama only audits within 3 years.  However, there are exceptions, as shown on this website: Taxpayer Bill of Rights – Alabama Department of Revenue.  If you click on the link, you will see this excerpt:  

In most cases, the Department has three years from the date a tax return is due or filed, whichever is later, to audit your tax return and assess any additional tax, penalty, and interest due. A taxpayer also generally has three years to claim a refund of any tax overpaid. However, if the tax was paid by withholding or estimated payments, and you failed to timely file a return, any refund must be claimed within two years from the original due date of the return. This authority is granted under Title 40, Chapter 2A, Code of Alabama 1975.

There are, however, certain circumstances in which the time limitations to assess additional tax may be extended. Some of those circumstances are as follows:

1. The Internal Revenue Service (IRS) adjusts your federal income tax return and these changes affect your Alabama return.
2. You signed an agreement with the Department to extend the time period to adjust your state or local tax return.
3. You omitted more than 25 percent of the taxable base that should have been reported on your tax return.
4. You failed to file a return or intentionally misstated or fraudulently filed your tax return. (Italics added on points 3 and 4)

The point of highlighting these points is not to argue that Alabama is correct in its audit, but rather, the two most likely reasons that they are doing so.  If you wish to contest the audit, you would want to be able to prove that neither of these two points apply to you.  However, either point does (and what will especially be claimed by the state is point #4), then Alabama can go back more than 3 years to assess delinquent tax (and associated penalties and interest).