Try changing the filter EG depth parameter to start your investigation.

Although this preset is single-element, a secondary trance sound rises when the keys are pressed strongly. From which edit point might this preset be triggering this?

Those changes are due to the various elements Filter EG parameters. See p.105 of the Reference doc.

On my M8X the one element in that performance has FEG Depth set to +63 - the maximum. 

FEG Depth
Determines the Cutoff Frequency range for Filter EG.
Settings: -64 – +63

That value of +63 (it may be different on the classic Montage) means that the cutoff frequency change will be the maximum.

Change that FEG Depth to 0 and you won't hear the change you mention.

The other parameters on that screen also modify the extent, and rate, at which cutoff is changed.

Set FEG Depth back to +63 and look at the resonance parameter on the Filter Type screen. Change the resonance to +127 and listen to the sound when you press hard on a key and hold it. Make sure you turn down the volume first.

The combination of resonance and FEG Depth is what magnifies the change/rate of the sound you hear since resonance determines the bandwidth around the cutoff frequency and FEG Depth determines the lower and upper limits of the cutoff frequency change.

Reset the resonance and go back to the Filter EG screen.

Play around with: Time/Vel, Depth/Vel and curve and you will see that they modify the amount, and rate of the cutoff changes that are made for different velocities. Just change one parameter at a time and use different velocities when you play each test note.

So resonance and depth define the boundaries of the sound 'box' and the other parms determine the amount and rate that things change within that 'box' based on the actual key (see 'Center Key') and the velocity you play that key.

Let’s take the “Hyper Velocity AF 1” sound example in the synth bass category on the Yamaha Montage.

Thanks for providing a specific example - it makes it a lot easier to know what you refer to.

That is actually a GOOD example since it only has one part and one element yet makes some dramatic changes.

You didn't mention it but did you notice the AF1 in the performance name? That indicates the performance is using assign switch 1 in some fashion.

Go to the control assign screen (p.89 of the ref doc) and set the display switch to assign switch 1 and you should see that the switch also has filter cutoff and resonance as destinations. The shape of the curve (curve type) tells you what happens when that switch is used.

The switch is either OFF (full left of curve) or ON (full right of curve) - so when the switch is ON the amount of change will be based on the Y value (height) of the curve on the right side.

As shown on p.145 the switches can be either 'Momentary' or 'Latch' 

Assign 1 Mode/Assign 2 Mode (Assignable Switch 1 Mode/Assignable Switch 2 Mode)
Determines whether the [ASSIGN 1] and [ASSIGN 2] buttons functions as a latch type or momentary type.
Settings: Latch, Momentary
Latch: When set to “Latch,” pressing the button alternates the status between on and off.
Momentary: When set to “Momentary,” pressing/holding the button turns on and releasing the button turns off.

Make sure you turn the volume down and then press assign switch 1. Because a switch is an 'all or nothing' value you will get the maximum effect based on the curve type and parms.

The default setting for the switches is OFF and, by default, when you change performances the switches will be reset to their default as shown on p.170 unless you have changed the global value to 'hold' for all controllers.

  In such sets, I can’t fully control and understand the character of the sounds I can’t adjust myself.

I'm the same way. Sometimes the hardest first step is to isolate the things that are affecting what you are trying to understand. It isn't always easy to know what you can delete or ignore without accidentally modifying what you want to look at.

You are going about it the right way. I actually keep a doc file as a record of what I find when I do these tests so I don't forget things.