mkinitcpio shouldn’t factor into this at all.
There are a few things that matter:
- Taking a snapshot - This is what triggers the need for the menu to be recreated
- grub-btrfsd - This is what is watches for the new/deleted snapshots and updates the menu
- grub-mkconfig - This normally shouldn’t need to be run manually but if you do it will regenerate all the grub menus
In your case, I don’t think it is user error. I suspect something went wrong with either timeshift or grub-btrfsd