Need to log in twice for dkms-built kernel modules to load after kernel update

For the past several kernel updates, dkms kernel modules like the nvidia drivers or asus-wmi-sensors module fail to work on the first login after rebooting.

dkms status did not show the modules installed for the current kernel.

I checked journalctl and it showed no errors and even indicated that the modules loaded. Confused, I just logged out and logged back in (without rebooting) and everything works (graphics drivers work, psensors can read the asus-wmi-sensors, etc).

Checking dkms status again this time shows the modules installed for the current module!

What’s going on? Previously, I was doing dkms autoinstall and rebooting again, but it seems that was unnecessary.