I find that Pivotal is pretty opinionated with the workflow you use. Specifically, it is meant for an agile process that is exactly that Pivotal (the consulting group) uses to develop their client products.
* Pivotal Tracker is the SaaS software you're thinking of.
* Pivotal Labs is the agile and lean engineering/design/product/data science consultancy, from which Pivotal Tracker first emerged as a product.
* Pivotal is the parent company formed from Pivotal Labs and other products (notably Cloud Foundry, Spring, Greenplum, Gemfire) several years ago.
Disclaimer: I'm work at Pivotal Labs.
My first thought is we should add a "did you mean Tracker?" link somewhere, but that's got problems too. We work on a lot of software.
This is what I get for not pair-posting.