The way inheritance works for Splashtop is that the parent policy pushes its state down the tree, but the child policy can override the state of the parent when disabling the integration. Thus, enabling the integration at the parent level does not automatically push it to the child policies. Child policies have Splashtop disabled by default.
The Splashtop integration will not inherit into Child policies; it must be enabled per Policy where you'd like to use the tool.
This also means that if you want to enable Splashtop for a child policy, you must also enable it for the parent.