Yeah, to be clear, from the main mansion screen, click the occupation of anyone currently at the Mansion (by default, "Rest"). That will bring you to the occupation screen. You should have an icon for each of the quests that you can then assign workers to. It will take some number of turns to complete them (which can be non-contiguous, and/or with different workers).
The quests you list both use Physics, so workers with better Physics will make faster progress. Other quests you can get from the job board are similar but use Wits or Charm.