APM Network Access Split Tunnel: Not Seeing Lease Pool IP in tcpdump

just guessing, but as you trying to see traffic that is tunnelled and then forwarded internally perhaps it just where tcpdump is intercepting the incoming traffic i.e incoming interface still VPN. You can check you session in "Manage Sessions" to see what IP was assigned, also you could run an irule with log statement on the VS to see what client IP your internal VS is seeing, or if you have a route in place try hitting some other IP from your client and tcpdump for syn packets heading out of the F5, cheers