Triggers and Workflows will fire irrespective of the API you are using.
Form the link that you have shared please go to the section:
Although the flexibility of triggers is a great asset, triggers can cause many kinds of problems in your loads and integrations. Locks are one of those problems. When you’re loading records that fire one or more triggers, and any of those triggers performs either a select for update or a DML operation on records other than the record that you’re inserting, updating, or deleting, Salesforce locks those other records. These locks can in turn cause lock exceptions. Consider disabling trigger logic for your loads and integrations, or having a special, optimized code path for such activities.
When workflow rules trigger field updates, Salesforce locks the records that they update. And when multiple threads try to update the same records simultaneously, they can cause lock exceptions. Consider defining your workflow rules so that they don’t execute during loads and integrations.
Basically it implies that logic should be efficient enough to handle large data sets(Batch size).