can a Netgear router with parental controls access search history from an older router

My parents bought a Netgear router with parental controls (which I'm fine with, I'll just make sure I won't look up anything bad again) but I'm worried that the search history from the old router will show up on the new router's parental controls (the Netgear router), because they were on the same Wi-Fi network. So will the nighthawk parental controls show history from previous routers (that were on the same network) or just the history that went through the Netgear router alone?