While Alister and Zanna were discussing the Demon King approaching their royal carriage, the Demon King in question had already arrived in front of their royal carriage. Because of that, Alister had to pull the reins and halt the royal carriage.
If his target wasn't the Demon King, Alister wouldn't have halted the royal carriage.
The same went for the Demon King. If the Demon King hadn't encountered the royal carriage, he would have left the Demonic Impure Land unobstructed.
However, the Demon King felt the battle intent of Alister and Zanna and he knew that even if he wanted to take a detour and avoid the royal carriage, Alister and Zanna wouldn't allow it.
The Demon King already guessed that he was the target of these two powerhouses. But even so, the Demon King wasn't afraid.