Seems like $JOB is not working properly. I tried loading scene that is using $JOB made on windows, into Linux machine.
Nothing is loaded right away. Redshift proxy files can load but have to disable and enable every single one of them manually, but also textures and everything else is not loaded at all. $HIP seems to load right away if scene is loaded but using $HIP limits a bit custom project folder organizations.

In short, is there something wrong with $JOB and can it be fixed or we must use $HIP instead?
Is $JOB working as intended?

$JOB is associated with projects, and $HIP is associated with scene files. You have to reset $JOB if you move your project to another computer. On the new machine, use the File menu option Set Project... Browse to the root of your project and click Accept.

You can read about it here:
https://www.sidefx.com/docs/houdini/basics/project.html [www.sidefx.com]

Yea I know about that part and that is what I did. Reset project again, reload scene and still nothing was loaded. I still had to go to each redshift proxy and disable and enable. It is not that it doesn't recognize $JOB, it just have to be forcefully reloaded, even after setting $JOB project again.

edit:
Ok actually this was the process I had to do:
Set project on Linux machine
Load scene
Set project again
Save scene, load scene and then it loads everything.

It's a bit messy and also makes it impossible to submit scene to rendering on deadline from win machine and to render on Linux machines as well or vice versa.
Seems like reorganization and using $HIP instead is safer, more stable and predictable option..