Your setup is different. Your ASUS is your private network, and you do not want anyone into that. Also (I assume) you are not running chilli on the ASUS, but on your Linksys.

For what you want (unlike case above) you just setup your Linksys as normal: Setup as Gateway, (which is default), but with a different subnet than the ASUS (which you did), activate DHCP client on WAN and DHCP server on LAN (at first) and connect the Linksys WAN to the ASUS LAN. Next setup chilli and hotspotsystems as normal (which deactivates DHCP again.

For your setup, you should not be confused with this thread. This thread wanted *both* devices as hotspot, you want one as private and one as hotspot.