IF it is authentication problem, then the problem is not with VLAN assignment. Because, VLAN assignment occurs only after authentication. So, send me the debug dot1x auth or debug dot1x aaa auth command output for verification.
Is your switch port, where your AP connects to the wired network, configured as a trunk? You will need that in order to transport traffic to and from the VLAN other than the native VLAN.
Also, I have faced problems with dynamic VLAN assignment when multiple BSSID is configured on the AP. If your encryption settings are the same and you are using the same AAA servers, you will be better off using one SSID.