For the Observation Training, your worker seems to work X tasks in a row when you manually click them to assign a task, where X is their "Observation Training" level.

So that automates their work if you assign it to them manually.

The self-starter training seems to take effect when you've not manually assigned a task to them. They will search for a single task to complete X times in a row, with a slight delay between each task, where X is equal to their "Self-Starter Training" level.

When their tasks are started automatically via this skill, the "Observation training" seems to be ignored.