I took the first test just like the OP, the logical reasoning part seemed kind of irrelevant and a waste of time for me. That was nothing compared to the second online test.
The environment of the second test was like a scenario out of Black Mirror. Not only did they want to have the webcam and microphone on the entire time, I also had to install their custom software so the proctors could monitor my screen and control my computer. They opened up the macOS system preferences so they could disable all shortcuts to take screenshots, and they also manually closed all the background services I had running (even f.lux!).
Then they asked me to pick up my laptop and show them around my room with the webcam. They specifically asked to see the contents of my desk and the walls and ceiling of my room. I had some pencil and paper on my desk to use as scratch paper for the obvious reasons and they told me that wasn't allowed. Obviously that made me a little upset because I use it to sketch out examples and concepts. They also saw my phone on the desk and asked me to put it out of arm's reach.
After that they told me I couldn't leave the room until the 5 minute bathroom break allowed half-way through the test. I had forgotten to tell my roommate I was taking this test and he was making a bit of a ruckus playing L4D2 online (obviously a bit distracting). I asked the proctor if I could briefly leave the room to ask him to quiet down. They said I couldn't leave until the bathroom break so there was nothing I could do. Later on, I was busy thinking about a problem and had adjusted how I was sitting in my chair and moved my face slightly out of the camera's view. The proctor messaged me again telling me to move so they could see my entire face.
The whole experience was degrading. If you're wondering why I did it, well, I've been using various AWS services for five years and I admired the work that the AWS team had done. Furthermore, I need the income to support my parents and Amazon was the best chance I had at the time. I got invited to do an on-site interview but I declined once I had another offer, and I'm glad I did.
EDIT: Small detail I forgot to mention. When I was showing them my desk, I had the monitor for my desktop (I was using my laptop for the test) and they asked me to turn the monitor so it was facing backwards.