The quoted sentence places no restriction on its benefit, and says nothing about initiation. It should apply as of character creation.

Following your interpretation, a mystic adept with magician's way (rather than "uninitiated magician") should use initiation exclusively for [adept-only metamagic][1].

However, "free use of all regular metamagics" is a very powerful feature that people would talk about in online discussion forums. [They don't][2].

It's also problematic from a game balance perspective. Should a character instantly become more capable whenever you buy a splatbook?

Therefore, logic indicates that the RAW phrase "have access to" means RAI "are allowed to purchase". When the sentence is viewed as a redundant restriction on physical adepts, the rules are consistent, although worded poorly.

  [1]: http://rpg.stackexchange.com/questions/27290/how-do-mystic-adepts-gain-power-points-in-shadowrun-5
  [2]: https://www.google.com/search?q=shadowrun+mystic-adept+magician+way+grimoire+OR+sg