If you read the Reconstruction acts, what was being readmitted were the delegations to Congress, not the states into the Union. There is no evidence of any enabling act, the formal process of admitting a state to the Union, for any of the Southern states after the Civil War.
Why then were Texas, Virginia and Mississippi not able to participate in the 1868 election? Was the readmission of the congressional delegations a prerequisite for their electoral votes to count?