Using Rick's idea to see what is happening during the transition frame by frame, I mimicked the first transition in the video using annotations (callouts) with animations. Note that I didn't have the same fonts available. but other than that it is close to the original. https://www.screencast.com/t/CAKjALtl
Animations are the real powerhouse in Camtasia. Most parameters are animatable over time and that allows you to do some very creative things. Here is the project if you want to see how it was recreated. https://www.screencast.com/t/16yLlo0aTRo
Since none of the animations were linear, we needed a lot of single frame animations to mimic the original. If you've never worked with groups, click the plus button at the bottom left of the group to expand it in another tab on the timeline. There you can see the all of the annotations and animations.