Adaxes itself doesn't store the password for the Adaxes service account. Adaxes service is installed as a Windows system service that runs under the account of the Adaxes service administrator. The logon information for this system service is specified during Adaxes installation and is stored by Windows.
Credentials for managed AD domains are encrypted using the Data Protection API (DPAPI) provided by the Windows operating system. These encrypted credentials are stored locally on the computer where the Adaxes service runs and associated with the account of the Adaxes service administrator, which means that only processes running under this account can unprotect the data.