To get the reward for your Temporal Agent on the Delta Story Arc I found that you must, complete the full arc including the all ground missions on Kobali Prime before being able to get the agent reward. Although you can complete the arc without doing the ground missions, when it comes to the recruit rewards all the missions have to be done before you can claim the reward. I know this is the case with the temporal agent as I did it last night. I do not know if the same conditions apply to Klingon or Delta agents yet.
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Once the accolade is started, it will list the missions required to complete it.
The Delta Quadrant story-arc does indeed require all of the Kobali Prime missions that make up the Act 1-3 wrappers.
Although there are a handful of 'found' missions that are not required, these are not part of the Act 1-3 chain.