Where does the Plymouth theme come from?
There are a number of plymouth themes available from the Ubuntu repositories. When you install plain Ubuntu desktop, the package "ubuntu-desktop" will install the package "plymouth-theme-ubuntu-logo" which is the plain Ubuntu plymouth theme.
When you install Kubuntu, the package "kubuntu-desktop" will install the plymouth theme "plymouth-theme-kubuntu-logo".
If you have more than one plymouth theme installed, you can choose your preferred one with:
sudo update-alternatives --config default.plymouth
Note that this applies to the plymouth graphical theme. Plymouth also has a text theme which should only show if graphics are unavailable. The same applies, but the package names are a bit different and the update-alternatives entry is "text.plymouth" rather than "default.plymouth".
How do I make it take effect at boot? / Why do I only see my new choice at shutdown?
For the bootup sequence, plymouth needs to load before the root file system is mounted, therefore it needs to be present in initramfs (the initial ram filesystem).
The reason you are seeing the correct splash at shutdown is that you have update plymouth's configuration successfully, but the same configuration hasn't been placed into the initramfs.
To update the initramfs, you use the command:
sudo update-initramfs -u