When you link a Private DNS Zone to a Hub VNet and that Hub is peered with Spoke VNets, the resources in the Spoke VNets can use the records in the DNS Zone. This happens because VNet peering allows the DNS resolution to flow through the peered networks. You can find more details in the Microsoft documentation here: Virtual network peering.
Now, if you link the Private DNS Zone to a Spoke VNet instead, and that Spoke is peered with a Hub (which is also peered with other Spokes), the resources in other Spokes won’t automatically resolve records from that DNS Zone. The resolution only flows “downstream” from the linked VNet to its peers, not the other way around. For more clarity, check the Azure Private DNS documentation here: Azure Private DNS.
About the DNS servers setting in the linked VNet yes, it can have an impact! If you customize the DNS servers in the VNet, Azure Private DNS resolution might not work as expected unless those servers forward requests to Azure’s default resolver (168.63.129.16). The official guidance on this is here: Name resolution for resources in Azure virtual networks.