Minimal volume is not a homeomorphism invariant. It is shown in [L. Bessières, [Un théorème de rigidité différentielle][1], Comm. Math. Helv. **73** 443-479 (1998)] that the minimal volume of the connected sum of an exotic $7$-sphere and a closed hyperbolic manifold $M$ can be larger than $\mathrm{MinVol}(M)$. An online exposition can be found in section 3 of http://bremy.perso.math.cnrs.fr/smf_sec_18_07.pdf. 

As to what Wikipedia says, some people use the phrase "topological invariant" to mean "diffeomorphism invariant". Here "topological" is contrasted with "geometric".


  [1]: https://dx.doi.org/10.5169/seals-55112