After purchasing a tax deed from the state of Alabama are you obligated for any given time period to allow the original owner to redeem?

I understand from your question that the property was sold at a tax sale, that 3 years has expired since the sale and that you have made a purchase from the State.  You have what is commonly known as a "tax deed".  Such a deed does not convey good title -- that is, insurable title.  You have merely received whatever interest the State had. If the property is vacant, you are entitled to take possession of it.  After 3 years of adverse possession, you can probably be successful in getting a court order showing that you are then the owner of the property and at that point, you will have good, insurable title.  If the property is occupied by the owner that lost the property in the tax sale, or his/her heirs or family, the passing of 3 years has no meaning.  They will still have a right to redeem.  You have the right, of course, after getting your tax deed to demand possession but, when you do that, you will almost certainly encounter resistance which will most likely end in a redemption of the property. It is rare that a tax deed will ripen to good title.