All of the traffic to those sites, whether it is data or management traverses that tunnel.
To minimize the traffic, you could:
- Suppresss Broadcast traffic on wireless (config t wlan virtual ap <vap> broadcast filter all)
- Suppress Broadcast traffic on the wired interface of the RAP by enabling bcmc-optimization on the VLAN interface (config t interface vlan 10 bcmc-optimization)
Suppressing broadcasts on the VLAN interface also suppresses broadcasts on the wireless, as well.