How to tail a fixer
When you join a match, you'll start several hundred metres away from your target. Depending on your opponent's skill level, they will either try to flee or find you, with more experienced players looking to get as far away as possible.
The best way to tag a fixer without being profiled is to drive until you're within around 150 metres of them, get out the car and walk the rest of the way, preferably taking back alleys and scenic routes on your approach, as they'll be looking for you, too. If they drive away once again, get back in a car and catch up, but don't drive at full speed, as there's a chance they'll stop at random in an attempt to catch you driving like a crazy person to easily spot the non-AI driver.
You just have to spot your fixer in order to begin the tail, after which they have to remain in your field of view for the progress bar to keep moving.
Stay as far away from your fixer as possible. Players tend to look within their immediate vicinity when trying to spot their tail, so keeping your distance helps. Try and hide somewhere, rather than blending in, as players tend to sprint around trying to scout as many NPCs as possible.
Hiding in cars isn't a useful strategy as once you're in the car, you're stuck there because getting out and moving will give away your identity.
How to not get tailed
Unlike in Online Hacking, you don't have to remain inside the purple zone to play the match. The purple zone is simply to show you an area where your tail is.
As soon as somebody invades your game, and the purple circle appears on the map, get in a vehicle and drive several hundred metres away. The tail will try and catch up to you, so get out and find a good vantage point with a view of the road you just came from. Look for any car that drives differently to the standard AI.
This is the best way to quickly spot your opponent, and gives you a good chance to kill them before escaping. If, after fleeing, you fail to find the tail, flee again and see if you can catch them out on the second attempt. Keep trying this tactic until you catch them.