At some point in the game, you start getting bribes of 5 credits for every 2 immigrants you detain. Whilst slamming the detain button as soon as you see it is easy, it often takes a while to get a suspicious character out of my booth. Given that you don't NEED to detain people, doesn't it make more economic sense to always reject their visa and get 5 credits per immigrant, rather than 2.5 with detaining?
I'll consider it as the game is in end-game state, with the blue stamp and distant guards.
It takes about 10 seconds after pressing the detain button for the guards to have removed the person from your booth and you being able to press the button for the next person.
This means that the income from detaining equals being able to handle a person in 20 seconds from speaker to speaker, or equivalent to processing 18 persons/day.
Conclusion: Detain, not Reject.