Author may self-archive an author-created version of his/her Contribution on his/her own website and/or the repository of Author’s department or faculty.
And here is the quote from the second source:
Authors may self-archive the author’s accepted manuscript of their articles on their own websites. Authors may also deposit this version of the article in any repository, provided it is only made publicly available 12 months after official publication or later. He/ she may not use the publisher's version (the final article), which is posted on SpringerLink and other Springer websites, for the purpose of self-archiving or deposit. Furthermore, the author may only post his/her version provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be provided by inserting the DOI number of the article in the following sentence: “The final publication is available at Springer via http://dx.doi.org/[insert DOI]”.
Do I understand correctly that I can put my own version of the manuscript at my own (or my institute's) website immediately after acceptance, but I can submit it to arXiv only 12 months later after official publication? If so, it seems to me it doesn't make sense. If the manuscript is made publicly available just after acceptance at my own website, why cannot it be made publicly available at the same time at arXiv?