Whenever I use the word "after", does it imply that the work is complete?
Yes, it does in this context. Used as a conjunction here, it has a similar meaning to "following" or "subsequently." It doesn't mean that an action is completed in all contexts, but has been used here to describe what was done following their work. Ex: After eating dinner, I went for a walk outside. Ex: Don't watch tv until after you've finished your homework!
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