It's intended to mean that the finished product has not been tested on animals by the particular manufacturer. However, there is no legal definition of the meaning of the phrase, not least because different countries have different interpretations of what the phrase should mean to them.
In no sense can you regard it as meaning that none of the ingredients has ever been tested on animals by anyone ever.
No company could make such a statement because such a definition is simply impossible for anyone to confirm.
In general, these statements are made to assuage the concerns of animal welfare groups and others who are rightly concerned about animal welfare. The problem that keeps raising it head with many of the products that contain these statements is that people have different views on what they find acceptable. For example, some people would find testing a new skin cream on a shaved area on the back of a rat acceptable but others would not. Your definition of testing may not be the same as the next person.
Because it's impossible for the public to establish if any of the ingredients have ever been tested on animals, you'll never be certain. There are academic web sites that do index this information but they are not accessible to the public and will not come up in a standard web search.