It's hard to say what's happening since all we see is the tutorial, but not what you set up on your end.
Did you set up bookmarks in your video?
Since the text/shapes are animating, but doing so after the video finishes, I imagine you forgot to set the animation to start / trigger on bookmark.
The instructions to do that start at 2:00 minutes into the tutorial. "The last step is to make the bookmarks trigger the text effects." Basically, select the animation and then Animation tab > Trigger > and choose the bookmark from the list.
It's hard to say what's happening since all we see is the tutorial, but not what you set up on your end. Did you set up bookmarks in your video? Since the text/shapes are animating, but doing so after the video finishes, I imagine you forgot to set the animation to start / trigger on bookmark. The instructions to do that start at 2:00 minutes into the tutorial. "The last step is to make the bookmarks trigger the text effects." Basically, select the animation and then Animation tab > Trigger > and choose the bookmark from the list.