Hello guys, thank you all for your answers.
I have been searching for 3 days to understand what was wrong. You will not believe this.
I bought an epson with tank ink system and ... it worked. The ink is fine, paper is fine, everything is fine.
THe brother J4120DW has a piezo printhead. I didn't stop there, I managed to contact a friend who is working in brother company in europe (administration field). His answer is the following:
"The printhead of brother is actually piezo but some machines are using heat to print (it's not a total electricpiezo, it's a combination between both). What you had is just the sublimation ink is sublimating everytime you print on a paper, that's why it's not working (that's why they are making a brother ink). It's like it is sublimating on the paper."
I don't really know if this is what's happening, because the printer doesn't have a temperature of 356°F, or when the ink is not on a sublimation paper it can sublimate with a little heat, I really don't have the answet. I didn't try to ask again since he's not really in the technical field of brother.
Anyway, for any reader, if you want to use epson for sublimation, buy epson ink. If you want a brother printer for sublimation, use brother ink.
(I'm making drawstring backpacks with a friend hope you like ^^)