Yay, Klaus! Way to fight against Lucrezia's instructions! It's a good thing she's not there to block his improvisations, but then, I still think she's the one bringing the monsters and forces from Strumhalten to attack Mechanicsburg...
It is even worse if you take a broader view. At that point Tarvek pretty much had control of everything. Lucrezia-in-Agatha was out. The Geister leadership was down. Anevka was neutralized, and the Lucrezia in the robot head was locked in a box. He could have stepped out of that room and taken over Strumhalten without much problem. Except - and this is where his motive comes in - he knew Klaus knew something was going on there and an examiner would be coming to find out what. Tarvek needed to disappear, he needed to keep learning Lucrezia's secrets both to further his ambitions and to have any chance of getting her out of Agatha, and he needed a reliable, super-intelligent Anevka to explain things and deflect all suspicion as to what had really happened. And within the constraints he was working under at the time, that meant Lucrezia.
Also, don't forget, he CAN verbally control Anevka's body. He gave himself a trump card he can use that will take robo-Lucrezia out whenever he plays it. Assuming she isn't sneaky enough to examine that robot body and find and correct that little defect, first. Tarvek is playing both a short and long game, and he's always trying to give himself every advantage in both he can...
Naw, the Jagers learned to do this from them.