I do not believe Lifesteal in general is classified as a proc. Plus, spirit lifesteal also works with health swaps like siphon bullet, mirage scarabs and I am assuming Geist ult.
Procs would be something like Imp Burst (altho I dont think this is technically a proc either, but rather an if/than event. Lucky shots is a proc)
Proc has become a generic term for applying on hit effects in general even though thats not what it means.