The world border warning effect only displays when very close to the border, but does not show up at all otherwise. This was tested with the Vignette effect of BetterHUD on. With BetterHUD toggled off, the effect works normally; when toggled on, only standing next to the border triggers the effect.

Also, the FPS meter turns red while tinting, whereas other white UI elements from other mods do not change color (other mods not shown in GIF).

This was on 1.12.2 with the latest BetterHUD and no other mods were used.

I made sure the warning setting was >0 blocks and that in vanilla, the warning showed up even while not hugging the border.