To be more explicit; lets say your second catalyst switch is only used for VLAN100. You don't have VLAN100 configured on this switch, or any other config. It has the default config.
You currently have (lets pretend) port two of your MX250 configure as an access port in VLAN100 plugged into this switch. When you add the second MX250 as a warm spare, you plug the same port 2 on the warm spare MX into that same Catalyst switch.
Repeat for the other switches and VLANs.
You don't require links between the switches, because each single switch is dedicated to a single VLAN. Your solution is loop free so you don't have to worry about spanning tree.