Benji, Ostrom calls for “nested tiers [of governance] from the lowest level up,” rather than simply “control of resources at a local level.” Her model of control is much more complex than the traditional Socialist solution of “ownership of the means of production by the people.” She speaks not simply of who is in control, but of how the process of control is structured.
The classic “socialist” mistake comes from declaring “ownership by the people” but then having control at either too high a level (e.g. central planning) or at too low a level (e.g. collectives that optimize for local conditions without consideration of the non-local context.) Ostrom would oppose either of these errors.
Certainly, if one had a Socialist society, one could structure decision making according to Ostrom’s model. But, the same can be said for most other forms of society, most of which aren’t Socialist.