FSI hires both Sim and Ground instructors. In my experience as a customer, generally an employee will fill only one role (either sim or classroom), but I do know a few exceptions where sim instructors/checkairmen also teach systems classes.
For the most part, employment with any of the major sim training facilities (Simulflite, FSI, Pan Am, etc), instructors are required to be ATP rated, have real world experience in the type they are teaching, and often have type ratings when hired.
It's generally not your average "right out of college" instructing job, but rather a stomping ground for furloughees, retired corporate pilots, or folks that flew the line/corporate jobs for several years and decided to settle down in a "home every night" job.
The flight safety acadamy does hire CFIs/CFIIs off the street though for their part 141 training program.
Here's a typical simulator instructor job posting:
(This one from CAE Simuflite in Dallas)
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CAE SimuFlite, Dallas, Texas U.S.
Instructor Pilot – Hawker
Ref # S-06-155
Responsibilities:
Responsible for conducting classroom instruction in aircraft systems.
Responsible for flight simulation instruction including flight procedures & techniques.
Conducts pre-flight & post flight briefings.
Conducts pilot proficiency checks (CFAR Part 91 & 135) in the flight simulator.
When designated, conducts FAA type rating certification in the flight simulator.
When designated, assist with courseware development in the training program to keep courses up to date, accurate & responsive to the client’s needs & desires.
Qualifications - Required:
Meets FAA ATP Requirements.
Excellent classroom presentation & interpersonal skills.
Ability to qualify as a Training Center Evaluator (TCE) under CFAR Part 142.
High school degree or equivalent.
Computer & knowledge of internet applications.
Must be able & willing to work flexible hours including nights, weekends and holidays.
Qualifications - Preferred:
Type Rating in at least one of the following aircraft: Hawker HS-125/BAe-125.
Operational experience in type.
Bachelor’s Degree.
CFI and CFII.
Simulator, aircraft and/or ground school aviation instruction & evaluating experience.
Above average verbal & written communication skills.