You are right about the reference. However, "Cat-in-the-Hat moment" is not a fixed expression, as far as I know. We can't tell you what part of the story this alludes to without more information about what is being discussed. In other words we need Context and Background.
I am reading a book on system development. There written is a story, like this.. Jack was working on a project building an IT system to a customer's request. He decided to split the whole project into two phases: Phase 1 and Phase 2. Right about the time Phase 1 was almost completed, a colleague told him that the customer would not accept the system in phases. The customer needed to get the entire thing, Phase I and Phase 2 (kind of like Thing 1 and Thing 2 from The Cat in the Hat ).
This episode in the book has a title, saying "A Cat in the Hat Moment: Phase 1 and Phase 2." On the youtube some people upload videos titled like "A Cat in the Hat Moment." I have not read the book, nor have I watched the film. But I noticed that Thing 1 and Thing 2 are together all the time.
Maybe the situation that Phase 1 and Phase 2 should never be split is appropriate to be called "A Cat in the Hat Moment?"
I believe that you have it. Another fact about Thing 1 and Thing 2 is that together they made a mess and caused a lot of trouble, until finally the children caught them and put them out of the house. I don't know whether that would be relevant.
(Even though it is a children's book written in very simple language, The Cat in the Hat is fun to read. If you ever have a chance, you could take a look at it.)
The phrase "XXX moment" is used to refer to a moment when XXX happens. For example, the common saying "Aha! moment" refers to the instant when someone finally understands something and says, or thinks, "Aha!" One might say "When Bob saw Mary in the corner with Dave, it was his Aha! moment that Mary didn't love him."
So, there is a moment in these videos that reminds their creator, in some respect, of something in The Cat in the Hat. It may well be the moment when Jack found out that Phase 1 and Phase 2 can't be separated, any more than Thing 1 and Thing 2 could be. The important thing to understand in the title is that it refers to a single moment - not to a process, a situation or an activity.
Now I know why the story has that title. In Japan "A Cat in the Hat" did not show on the theater. But the DVD version of the movie is selling here in Japan. Maybe the English in that book is interesting.