For me, individual tournaments are more about personal performance. Win or lose, how well did I handle certain types of positions or the clock etc. Sometimes you win a few, sometimes you lose a few. I don't worry about 1 tournament.
If we're talking about all the tournaments over a month or two, then yeah, I'm looking at my rating.
It's not all cut and dry like that. Higher rated players see a lesser impact for the same level of performance (let's say, half a point above expected value in a 5-round tournament) than lower rated players. If your "expected score" is let's say 2.5 based on opponents, and you score 3, you might gain 10 points if you are 2150, but 30 points if you are 1000.
More often, people are looking to reach certain plateaus. In the US, there are "classes" at each 200 level. You reach 1200, you are Class D. 1400, Class C. 1600, Class B, etc.
In my case, I have a tournament this weekend. It's not about whether I gain or lose a certain number in this tournament. I basically need about 21 or 22 rating points to reach master for the first time (2200), so for me the goal is that, whether it be this weekend, or over the course of 4 tournaments gaining roughly 6 points per tournament.