I've always read "getting my work done" as similar to "pulling my own weight" or "doing my fair share." They're not supposed to be read literally, only to convey an overall sentiment.
When I managed my team, work was never assigned to an individual. It was assigned to the team and the team took responsibility for it. Individuals accepted responsibility for pieces of work as they completed prior work. If an individual wasn't contributing enough, either the team's productivity would suffer or other members of the team would step up to fill in the gap. If that that lack of contribution became consistent, I'd notice, either through poor team performance or conversations with disgruntled team members who were covering.
A lot of it was handled by feel and when a member of my team felt like he was accomplishing enough to keep the team performing well, s/he absolutely had the discretion to leave early. The key is that when the team is responsible, people are motivated very differently from when an individual is responsible. Your team members are often your friends whereas you might have a more combative relationship with your manager. No one wants to be the one that lets the team down. And, similarly, if a team is being pushed too hard, everyone will feel it and everyone can push back together. This makes it really easy to see, as a manager, when you're asking too much of people.
I'd say if you're looking for a healthy work environment, look for ones that emphasize team accountability over individual accountability and then try to find a team where everyone respects each other. That team is, more often than not, going to do well and you'll share in that success. If you have a slump, someone will cover for you. If someone else does and you feel up to it, you can go above and beyond for a bit. It's a lot easier to give that extra effort when you're doing well than it is when you're struggling.