This reminds me of an anecdote that I used to tell people to describe certain aspects of computer media and is somewhat relevant here. The story is oobviously 20 years old, and the facts have been changed to make my point:
My wife recently came back from Italy with a VHS cassette of an Italian movie that she wanted to watch on our VHS player at home.
I sent the cassette out to a local video conversion store, so that they could convert the VHS tape from PAL to NTSC.
When my wife played the newly converted tape on our home VHS player, she exclaimed: "But it is still in Italian!"
I have no experience with Turbo Tax. But I suspect that in prior years (especially prior to 2007) it was coded in PowerPC code.
In 2007, Apple converted its entire line of computers to the Intel CPU (from the PowerPC CPU), but in order to allow its existing user base to continue to use its PowerPC software, they included a transparent emulation layer in Mac OS X Tiger (Intel), Leopard, and optionally in Snow Leopard, called Rosetta.
Rosetta allowed users to continue to use their library of PowerPC apps without much problem.
Due to the expiration of its third party license, Rosetta is no longer included in Lion, Mt. Lion or Mavericks.
Moral of the Story: If the earlier versions of Turbo Tax are not Intel compliant, they will not run on your new Mac Mini, unless you install Snow Leopard Server ($20 from the Apple Store, by telephone orders only; part number: MC588Z/A) installed into Parallels ($79 retail).
If the latest version of Turbo Tax will open older Turbo Tax data files, this may not be a problem for you.
That is how I am able to continue to access my older Quicken Deluxe 2002 data files when necessary.