The VPN Clients will always get either the ASA as the default gateway or the IP Address they received via this vpn client connection, now to send all traffic from this clients back to your core router then you go ahead and configure your ASA to use a "tunnel default gateway" with:
route inside 0.0.0.0 0.0.0.0 X.X.X.X tunneled
This will send all traffic that is received via any tunnel back to your core router which should be the x.x.x.x