The behavior you noticed is intentional, and it's made to prevent the airplane itself to cut the follow me, so there's a bubble around the airplane, and if you go too close it will circle around you. Well, it's not so simple, it doesn't monitor just your distance, it monitors the closure rate, trying to anticipate when you will be in the future based on your current acceleration, because without a prediction and with a simple distance check, the car wouldn't have a chance to realize it's too late to prevent being crushed, because it has *its* own acceleration lag to contend with.
That's the complex explanation. The simpler explanation is: provided you follow it from a good distance and you keep your acceleration under control, you won't have any problems with it. Of course, the Follow me speed is customizable in the Settings, so you can just try with the setting that works better with your airplane and your taxi habits.
