I know in the case of movies or TV "watching" is used, but I have consulted some animation tutorials and in the description they usually write "viewing the animation", which is the right one for this case?
I'd suggest "view" in this case is verb definition 15 from dictionary.com:
to look at; survey; inspect
When you "view your animation" within a piece of animation software, you're inspecting it to see how it looks, to make sure it looks how you want it to.
When you're happy with it, create a final version, and sit down with friends later: that's when you watch it.
You have to remember that some words take on new meanings in different contexts, especially in areas such as computing, from which your example is drawn, because it has its own set of terminology. While most terminology is rooted in the original linguistic meanings of words they can mean something quite different.
From a purely linguistic point of view (no pun intended) the words "watch" and "view" have slightly different meanings. "Watch" suggests looking at something for a sustained length of time - for example you don't "watch" a photograph. Well, you could, but it wouldn't do much. But when speaking about TV for example the two words are pretty much interchangeable. Most people speak of "watching" television, but those who work in TV usually refer to their audience as "viewers", not "watchers"!
However, in many software applications the term "view" is used to describe a particular screen configuration. For example in Microsoft Word you have a view menu where you can choose to look at your work in Print Layout, Web Layout, Full Screen etc. As the screen configuration is called "a view" it is only natural that you would talk about "viewing" it.
Similarly, your example seems to be drawn from the documentation of a software package. It even refers to "the Animation view" which is the name of a view (note 'Animation' is capitalised). So it makes sense that it would speak of "viewing" animations this way. If this is an animation package for creating animated sequences, I am fairly confident that once you had exported the finished product and placed it on some common medium such as YouTube for example, people would talk about watching it.
According to dictionary.cambridge.org following are the verbal meanings of the words;
- LOOK AT (eg: You can watch the trains going by from this window.)
- BE CAREFUL (eg: You need to watch him - he's a strange character.)
- HAVE OPINION (eg: We view future developments with some trepidation.)
- SEE (eg: You can view the sharks from outside the glass tank.)
"viewing the animation" implies watching the animation then having an opinion over it.