Of course the warmup stage has nothing to do with the remote.
The Logitech Harmony has as a central concept a set of activities. Each activity, whether watching TV or listening to music, has a set of devices associated with it, and a desired state for each of those devices.
For something like an AV Receiver, or, say, an Integrated Stereo Amplifier (like the LIO), the Harmony expects to set the LIO to a specific input.
Most devices that the Harmony expects to control do not have a long warmup stage. So by default, what will happen when you include the LIO in the "Listen to Music" activity, is that it will turn on the LIO, and if needed, it will cycle the inputs into it gets to the right input. If I recall, the warmup stage precludes any other activity, including switching of inputs. So in this case, what will happen is the Harmony may try to switch inputs, but nothing will happen, and then the Harmony and the LIO will be out of sync.
Having said all of that, the Harmony let's you program delays into each step. So a LIO owner with a Harmony remote can manually tune this configuration if needed.
Wilson