Cisco inter-vlan routing behavior without L3 default gateway

I am an infrastructure systems person who occasionally plays the role of a network engineer. I was reviewing some configs with the staff network engineer. One thing that stood out to me that I did not understand:

Inter-vlan routing is working for clients without the default gateway on the client being the switch's L3 interface on the vlan.

Example:

Switch A as 2 VLANS with a L3 interface in each vlan. Vlan 10: 10.0.0.10/24 Vlan 20: 10.0.1.10/24

Router B has a L3 interface in each vlan. Vlan 10: 10.0.0.1/24 Vlan 20: 10.0.1.1/24

Client C is in Vlan 10 with an IP: 10.0.0.50/24 and default gateway of the router (10.0.0.1)

Server D is in Vlan 20 with an IP: 10.0.1.50/24 and default gateway of the router (10.0.1.1)

There are no additional routes configured on the client or server.

When I trace traffic going from Client C to Server D, it never traverses the router. My network engineer says this is because inter-vlan routing is turned on. These seems to defy routing 101: I would have assumed that the client would need the default GW to be the L3 IF of the vlan it is in (or something proxy arping into it) for inter-vlan routing to work? That is how I have always configured it for my entire career.

My background is more Juniper and these are Cisco switches so I am not so familiar if this is something Cisco-ey going on or there is a protocol that enables this that I am not aware of?

Thank you for any pointers on this.