I recently started with a company who has several offsite & out-of-state (various states) employees who work from their homes. Does the company need to get separate workman's comp insurance?

Yes, unless you and the other employees in your state are exempt (under the law of your state), your employer needs to have workers compensation insurance for its employees in your state.

Aside from the different states already answered:
Employees working at a desk at home are as low a risk as can be and are rated as such. The comp auditor will set the rates for each category. Anyone who is an employee has to be covered by comp. If they are not an employee, they are a contractor, and contractor is a term with many IRS requirements, only one of which is not working on the company's property. Another (of many) is that the contractor have his own insurance, and another is that he have more than one work source of income.
Maybe you know this; wasn't sure.