Perhaps Zane is a big fan of Syrus himself and by reading the fanfiction, he gets to delve deeper into the Syrus - centric stories. It could also be that he enjoys the creativity of the fanfiction community and how they expand on the Syrus character in ways the original work might not have.
There's no way to really say if it's common without knowing more about Zane. If he has a lot of free time and is a die - hard fan of the source material involving Syrus, then it might be a regular pastime for him. However, if he's not that into the whole fan culture or Syrus specifically, it would be less common.
At first, their relationship might become strained. Zane's anger could make Syrus confused and a bit scared. Syrus might try to avoid Zane, not knowing how to deal with his anger.
One possible reason could be jealousy. Maybe Syrus is getting more attention in the fanfiction world, and Zane, being a proud character, doesn't like that. For example, if Syrus is praised for his skills while Zane feels overlooked, it can make him mad.
Zane might start by assessing the situation. If they're in a dangerous place, he'd be very cautious. He could also be a bit impatient with Syrus at times, but still try to keep him safe. For example, if they're in a dungeon - like area in the Duel Academy, Zane would quickly find a way out, pulling Syrus along if he has to.
In the Yu - Gi - Oh fanfiction, when Zane gets stuck with Syrus, they might have an intense duel training session. Zane could be super strict with Syrus, pushing him to improve his dueling skills. Maybe Zane would share some of his top - secret dueling strategies that he's developed over the years.
Maybe he'll be really bored at first. Fanfictions can be quite strange sometimes, especially if it's not something he's interested in. He might try to find a way to stop watching, like looking for an exit button or asking someone for help.