Connected wifi clients are tagged with VLAN (if assigned) and dropped on the
AP switch, which registers the client device MAC addresses. The connected
clients do an ARP with DHCP when they are successfully authenticated, so the
switches/routers are maintaining L2/L3 tables.
An advanced option under WLAN, is to enable Proxy ARP, whereby the AP will
respond to wired side ARP requests toward any connected wireless client. For
WLANs tunneled to the ZoneDirector, the ZD can perform a dhcp relay.