Hi guys, I actually found what the problem was.
When the display is plugged in, the framebuffer goes in simple buffer mode. When Qt/EGL starts up, it switches the framebuffer in double buffer mode.
But, as our Qt app is rebooting the display at startup, the framebuffer goes BACK in simple buffer mode, while Qt thinks it is doubled. Then, as the FB is in simple buffer mode, the buffer swapping has absolutely no effect. In parallel, Qt still tries to write the second buffer, which will actually never be displayed.
Then, I modified the HDMI driver to make the FB always go in double buffer mode.
Thanks anyway for helping !