I’m pretty sure I get the additional rewards even if I’m too late.
Checking it with another mission (same NPC), let’s see:
NPC: Nebraska / Geda / Rimwaa (107)
Mission: Freight Captain required: Apply Within / You know the drill! (114)
Promised reward: 3102 cr + 470 cr (15 min)
Loaded freight, jumped to Greenfield, waiting… waiting… delivered:
"You had this cargo on-board for 0 hours, 18 minutes, 21 seconds"
Back to Nebraska:
“Congratulations, you made it back in time for the bonus. An extra 470 credits have been deposited into your account”