mtune=... does NOT affect the instruction sets used, or machines the executable is run on.
For that (eg, enabling SSE), you'll need march=....
If you do march=core2 for example (on a new GCC), it will use all the instruction sets available to Core 2 CPUs. march=x also sets mtune=x. The executable won't run on older CPUs.
If you ONLY use mtune=core2, it will generate code that runs the best on a Core 2, but will still only use instructions available to all x86 CPUs (eg, no SSE), hence it will still run on old CPUs, just a little slower.
As a real world example, I think a few years ago some Linux distribution decides to use -march=pentium3 -mtune=pentium4, or something like that. That means, the code is guaranteed to run on a P3, but optimized for a P4, since they predict most people will be running for a P4.
If you don't use any flag, GCC will assume -march=i386 (lowest x86).