I need to let remote VPN clients to connect to Internet from the same ASA VPN server
" client connects to ASA through VPN tunnel from outside interface then access Internet from the same ASA from outside interface again
you'll need to configure 'same-security-traffic permit intra-interface' on the ASA .
Also, need to setup the corresponding nat statements for your clients pool range.
global (outside) 1 interface
nat (outside) 1 access-list anyconnectacl
where anyconnectacl is the pool for your clients:
access-list anyconnectacl permit ip 172.16.1.0 255.255.255.0 any