I think he might be referring to the Player as the ‘pedal’ in that example.
when the Rig Manager and the device are connected properly changes made on one will be refletcted on the other.
One thing to keep in mind, and forgive me if you already know but sometimes it’s the simple things that get overlooked, there is a difference between a rig and a profile. When you say ‘the amp’ isn’t the same it is possible to audition profiles (amp and sometimes a cab) you find in Rig Manager that are not on your device nor are they in your local library of rigs. So you can be temporarily listening to a different ‘amp’ that doesn’t get saved to your device or local library (your computer)
not sure if this applies to your situation or not, sorry if it doesn’t help.
save to local library and build a rig with the new profile in it should get you there