Linting takes as long as it takes for processing-java to compile, usually around 2 seconds. So after saving, errors will be marked with a slight delay.
On first activation the plugin will install all dependencies automatically. processing-java has to be installed manually.
In order to make sure $PATH is set correctly, you should run Atom from the command line!!! (This is important, elsewise it won't find processing-java).
You can configure linter-processing by editing ~/.atom/config.cson (choose Open Your Config in Atom menu):
Make sure to link the processing-java command correctly. Installation process of processing-java can be seen here: https://atom.io/packages/processing
Good catch. Let us know what about this package looks wrong to you, and we'll investigate right away.