Hi Slowhand,
The only triggers in that mission are "Reach a specified area", which is marked with a green arrow. You simply approach the arrows, getting close enough to each one to make it disappear. The text of the mission has timers. You may have to sit and wait sometimes, for instance, while being unloaded at the parts dock. Just sit tight, and wait for further instructions from the narrator/copilot.
The mission goes like this upon arrival at Fleet Bay . . .
Upon arriving at Fleet Bay parts dock, five seconds later it should say "You can park at the refueling pier.... Shut her down but don't get out, the supplies will be unloaded by the crew for you." Thirty seconds later it says "This shouldn't take too long.... I'll let you know when they're done and then we'll start up and head for Hunter Bay.... After you park, I'll get out and then be back in just a few minutes." Then the "parts dock" arrow pops up, and you go park there, where it points. Sit there, at the parts dock, for 120 seconds. Then the voice will speak again, saying "That didn't take long.... She's all ready to go... We're clear to begin our taxi out of the channel now." . . . and so on.