Tessa acted weird and did not want Arthur to know anything about what the vampire had told her. That only made Arthur's curiosity increase, and for that reason, he followed her.
With Arthur's power, following her would be impossible, but he was no ordinary vampire, and the inheritance from the Blood Monarch had many spells. Now that he had both parts of the inheritance, it was easier for him to learn such spells, especially with his blood essence.
He was there to be a spy, so the first spells he tried to learn were the stealth ones, which came in handy in that situation. One was an invisibility spell, but instead of using only mana, it also used the user's blood.
The blood would make the spell stronger, but Arthur would get weaker as time passed. Other vampires knew those types of spells too, but the one Arthur had was an enhanced version made by the Blood Monarch, making it stronger and decreasing blood usage.
"Where is she going?" thought Arthur as his body disappeared.