Can an E900 wireless router in bridge mode, having IP on a different net than the bridged network, cause problems due to this config?

I have an ISP-provided router with one available wired port, and wireless. Because the router is placed in a bad spot in my apartment, I have connected a Cisco E900 wireless router with a cable. This device is set to bridge mode. Originally, the ISP had set the local IP network to be the 192.168.0 network, and I had given the E900 a fixed IP of 192.168.0.2, which didn't conflict with any addresses used or controlled by the ISP router's DHCP server.

The ISP replaced their router, and the local network changed to 192.168.1. As the Cisco router is in bridge mode, I assumed that it would not be affected in any way by this, other than the web management interface no longer being accessible. I can actually access it by connecting to the E900 and adding an eth0:0 alias with an 192.168.0 address.

I am observing connectivity issues, which seem to me to be related to the wan-side of the ISP router. However the ISP support claims that my E900 router may have some (unexplained) adverse effect on the network. This seems implausible to me - but although I consider myself reasonably knowledgeable, I would never claim to be a network expert.

Devices connected (either by wire or wireless) through my bridge have no problem obtaining an IP address from the ISP router's DHCP server, and connectivity to the ISP router's web management interface is also fine, even in situations where the wan-link seems down.

Is my understanding of bridge-mode correct, that my router's 192.168.0.2 IP can't affect the ISP router, or should I set the E900 to use a fixed IP in the 192.168.1 range, or from the ISP router's DHCP service?

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