Joystics and slider doesn't work with time remap

Here is the situation: I created a test head rig for eye rotation using the Joysticks n Slider script in different head positions, which I successfully achieved. In my main composition, using the joystick, I can adjust the position of the eyes, and so that it doesn't lose its position when changing the position of the head.

•  All animating without any problems

However, the main problem arises: when I want to fixate the Time Remap at one position (no matter what it is, binding to a slider, entering an expression or manually setting frames), the joystick completely stops working.

• After fixating the Time Ramep, the joystic becomes useless

And from the outside it looks like that by fixating the position of Time Remap, I fixate the script itself, which makes it impossible to use the joystick.
To verify this, I created a test composition, where I created the simplest joystick, and it turned out that if you take the joystick from the pre-compose to the main composition, enter any expression in the Time Remap or set frames manually, then the joystick either stops working or does not work at all as it should .

• Only 2 frames for 1 position of the head. 

The first thing that came to my mind was to simply increase the duration of the layer to the nth number of frames so that we can animate in all poses.
Yes, indeed, this can be corrected with such a "crutch", but it seems to me that some other way out of this situation can be found.

In general, my main task is to make the joystick work regardless of Time Remap, i.e. for example, with a fixed Time Remap in a conditional 1 frame, I could easily animate the position of the eyes without any problems.

P.S. I'm newbie in this programm so some obvious things I can't notice due to the lack of experience.

I will be glad for any help