I finally found a solution but I unfortunately can't explain it. I discovered that the PC where I run my script is not important. How my MATLAB instance was launched is important.
I open my model from a third party software (RT-LAB from Opal-RT Technologies) and this software makes the MATLAB instance controllable from a script that is executed later. That is my solution.
I tried to retro-engineer how it is done but I couldn't. The only information I have is the command line from task manager:
I thought the important thing was "-desktop -MLAutomation -desktop -r" but it seems that the software does other things in the background with a temporary file. I found the temporary file and it was empty or maybe it's just encrypted. If I execute the exact same command line outside of the software environment, I get a regular MATLAB instance that I can't control with my script.
That only proves that executing script from command line to existing MATLAB instance is not impossible but pretty complex.
If anybody was ever able to launch a controllable MATLAB instance, please share it here.
Thank you!