Open source projects often have (and should, if they don't) a clearly published set of "community guidelines", which often includes a description of the project workflow and how contributions are accepted (and thus how they are tested), as well as the process for becoming a core committer.
As far as code review, again it depends on the community but the guidelines are often made clear. Some example guidelines for contributions by non-committers range from "working code wins" to "contributions must have full test coverage and documentation, with tests committed at the same time as the code" and everything in between; regardless of these guidelines, the one guideline that is implied is that the core committers will review any and all contributions from non-committers before accepting them.
Open source projects with groups of core committers also often have virtual meetings or dedicated time to discuss any contributions that may need extra sets of eyes -- much like the SE process of multiple close votes by users of a certain reputation before a question is closed, and the discussion of questionable things via meta or chat.
Here are a few quick links to some example community documents for projects I know best, where you can find answers to your question specific to these projects (you'll soon notice a theme):