If it is not possible to exhaust air to the outside then, air scrubbers (also called traps or negative air machines) must be used. If the air can be vented directly to the outside, then a plain exhaust fan can be used without any filtration. I really don't care what kind of space it is, if it's inside a building, I exhaust my work space air either through a HEPA filtered trap or directly to the outside. I see no reason to run negative air for three days if the containment is erected properly and the remediation is done correctly, UNLESS he has reason to suspect there may be a spore load outside of the remediation area that will be impossible to clean. That could be exposed fiberglass insulation for example that might have mold debris entrained in it, but was not part of the original problem. Then a flush with some forced air might be good. I would avoid anyone who wanted to do the job without any sort of negative pressure environment in his containment, trapped or not.
You have to wonder what good a containment is, if there is no fan to keep it negatively pressurized. For fun, ask the companies to see documentation that their trap has been tested. We checked a bunch of traps already and found about 90% had problems of some sort. Some that had never had the filters changed (years old). Some that bypassed up to 5% of the air around the filter because it was poorly installed. Some that the users had unhooked the magnahelic gauges that monitor the filter loading. And even some that had no HEPA filters in them. Just a pre-filter taped across the intake. Companies like these are in the "Mold for Gold" business and DO NOT have your interest at heart.