Well, no... see where I'm from, there are four dimensions separated by Summoning Methods: Standard, Fusion, Synchro, and Xyz. Everyone in each dimension focuses on their own summoning method and unless someone from another dimension arrives, the existence of other methods isn't really common knowledge. The only dimension that uses all methods is Standard, but since Jack is from the Synchro Dimension, he would only have Synchro Monsters like his Red Daemon's Dragon Scarlight.

[ Fusion Monsters aren't outdated at all! They're very powerful and Yuzu's used them really well. ]