Harvard referencing: same year, same last name, same initials

The guidelines to the venue you are submitting to must be your guideline. After all, the title of the paper is what distinguishes one author from the other. And this information is present in the bibliography.

For the in text references, neither University of Leeds nor The University of Melbourne has any suggestion for such situation. However, both use the style (Smith, 2012a) and (Smith, 2012b) for same author, different publications. So, that is not correct.

Personally, I would go with adding a footnote at every page that the citation occurs, maybe with a Google Scholar or personal website page. Writing the full name would not be a generic solution as there might be two different authors with same name and same surname.

Yes - the style is determined by the publication venue.

As someone who works with a bibliographic database (Mathematical Reviews / MathSciNet), I find brief citations systems that use last name + initials "quaint" at best. Yes, a human can possibly sort out whether A.B. Smith refers to Alan Brian Smith or Alice Beatrice Smith. However, if both are occurring in the references of the same paper, there is a good chance that the two Smiths work in related areas, making the identification of author with paper not so easy. There are harder cases to separate. In our database, we have over 100 names of the form Li Li and over 300 of the form Wei Wang (not counting names such as Weifang Wang). A favorite example of our catalogers are the two researchers named Angel Plastino and Angelo Plastino, both of whom work at Universidad Nacional Noroeste in Buenos Aires, who work in similar areas, and have coauthored at least 75 papers together.

I have very mixed feelings about bibliometrics, but many departments and deans do not. Trying to match A.B. Smith to the correct author for an automated publication count is going to be a challenge. Similarly, an automated match of the citation will be tough. Some citation styles for journals are particularly brief, something I associate with physics journals, but they occur more broadly. An example is the AIP "by number" style: initials and last names of the authors, the journal name, volume, first page number only, and year. AIP also allows a fuller style that uses the authors' initials, last names, title of the paper cited, journal name, volume, first and last page, and year. The brief style coincides with listing references in the order they appear; the full style is for when the references are alphabetical.

As an author, you are at the mercy of the journal style. If you have a choice, as with the AIP example, I recommend going with the longer version. If you are a publisher of journals with minimalist reference style, I recommend that you give your authors a break and consider switching to a longer style.