That's not true. The only scripting is the timer. The drones will show up at about 7 minutes remaining.The drones don't just show up after a certain time; when you approach the third base, they'll also appear, so make sure to clear out as much as you can of the first two.
I generally recommend hitting the first base as quick as possible and wiping it out, prioritizing the transport planes while they remain on the ground. Then clear out any fighters above you (they're worth points as well), then taking out the small convoy heading towards the second base for a few points, then heading to the refueling line (it's actually in-mission dialog that tells you that you can begin to use the refuel line; yes, the mission briefings are only good for the broad strokes of the mission, and do not inform you of the in-mission scripting). Then actually skip the second base (the one that's all canyon-y) in favor of flying to the third one. The second base doesn't have as many targets as the third, and with the canyons making approaches and strafing difficult, it takes more time to hit them.snip
If you feel up for it, there's special dialog that's triggered from flying through the small tunnel at the third base.
I think the drones spawn in closer to the second base than the third (it's been a while for me), so I think this strategy also buys you some time.
As NerfedFalcon said, try to use bomb special weapons over ground missile specials. Bombs deal damage in an area, so for weak and clustered targets like buildings, they'll blow through them faster. And using the machinegun well is probably the greatest difficulty curve for the entire gameplay, but once you get decent at it, it provides a ton of utility. However, I don't really recommend the A-10C, except for on Easy. AC7 is particularly bad about having a surprise air-to-air challenge in the middle of what's supposed to be a ground attack mission, and in this mission, that's the drones showing up. The A-10C is slow and terrible at dogfights, so you may manage to get through the mission with it only to be gunned down. Easy difficulty gives you enough health to just tank it, likely. But in general, the fastest plane that you can load up with the heaviest ground-hitting ordinance that you can refill at the refuel line is the way to go on ground attack missions.
If you've had limited exposure to flight sims (or using a standard controller for one), don't be afraid to play on Easy. Playing flight sims are not like playing other kinds of games, you're building new reflexes from the ground-up. Simply mastering flight is the biggest challenge, and it honestly took me a couple of playthroughs worth of AC5 to get pretty good at it.