Your device has the address 192.168.0.194 on the eth0 interface whose domain matches the router.
Your device also has the address 192.168.1.1 on the tether interface.
Your device knows that the exit route to the internet is 192.168.0.1 because the router told it through dhcp or you told it with the manual address assignment.
For a device 192.168.1.2 in the 192.168.1.0/24 domain to know how to go to the internet, it will be necessary to establish a route to 192.168.1.1. This is done by manually setting the tether connection parameters (gateway = 192.168.1.1) for the device 192.168.1.2. But this is not enough because it is also necessary to bridge 192.168.1.1. For example like this in the 192.168.1.1 device:
# bridge tether <-> eth0
echo 1 > /proc/sys/net/ipv4/ip_forward
echo 2 > /proc/sys/net/ipv4/conf/all/rp_filter
iptables -t nat -A POSTROUTING -o eth0 -j MASQUERADE
iptables -A FORWARD -i eth0 -o tether -j ACCEPT
iptables -A FORWARD -i tether -o eth0 -j ACCEPT