When entering a lesson or mission with throttle already engaged at some "inbetween" level, how do I "recalibrate" my throttle to reflect the proper throttle setting?
With your new Saitek Fly Joystick, you may be experiencing a similar, slight annoyance I have with my Saitek Cyborg Evo Force Joystick.
Every time I fire up my FS 2004/FSX I must first rotate the stick around all of its axis, and rotate the throttle throughout all its range then reduce it to zero, to centralise everything, otherwise it will assume some intermediate settings making the Aircraft difficult/impossible to control initially.
It seems common to Saitek, in that the stick does not assume a central position, and the throttle fully off, when the Sim is started!
Perform the above action before taking off, after staring the Sim, and the Joystick will operate correctly for the rest of the session...

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Paul... 8-)....!
Win 8.1 64-bit. DX11. Advent Tower. Intel i7-3770 3.9 GHz 8-core. 8 GB System RAM. AMD Radeon HD 7700 1GB RAM. DVD ROM. 2 Terra Byte SATA Hard Drive. Philips 17" LCD Monitor. Saitek Cyborg X Fly-5 Joystick. ...and a Briggs and Stratton Petrol Lawn Mower.