To put simply: Whenever you shoot an arrow onto a fire source (eg, campfire, lava, etc.), the arrow visually appears as if it's on fire before hitting the fire source itself. I don't know whether it has to be specifically a crossbow+soul campfire as shown in video, but that's just how it is for me
Link to video (can't attach because of size limit): https://youtu.be/EKPhpm1rafQ
I found this out accidentally
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This is because the visual position/animation of moving entities typically lags behind their server-side position (MCPE-179969), while the texture for things like being on fire updates instantly. For example, this also applies to hits (MCPE-109423) and explosions (MCPE-151881). So arrows and other projectiles catch fire when their server-side position passes through the fire.