I'm not 100% sure this is accurate anymore but the way tactics used to be rated was based on treating them like a player. They would get assigned an initial rating and if someone got it right, the rating would drop as if the tactic has lost to a player with that tactic rating. Same was true for a wrong tactic. So the ratings fluctuated based on that.
I think that is still true.
As to scoring you get:
https://www.chess.com/blog/News/chess-com-dev-update-april-28-2017
and
https://www.chess.com/blog/News/chess-com-dev-update-may-26-2017
There have been some additional updates for sure that deal with the tactic selection algorithm, though I don't know if there have been other structural changes. Early on (after the April 28th update) the algorithm made it really easy to get a high rating, it was tweaked and then it caused some deflated ratings and last I tracked it, I was getting about 60% of the tactics higher rated than my current rating.
I've been having massive (+/- 100 points) fluctuations in my tactics rating. I've noticed that sometimes I get a lot of points for super easy tactics, and other times I get 1 point for a super hard tactic I took too long on.
It seems the consensus on the forum is
1. You get more points for solving hard problems above your rating
2. You get less points for solving easy problems below your rating
If you take too long on either of them your points go down.
looking at some of the big wins (+13) I've gotten right, I don't see how many of them are considered "hard" tactics. Some of them are even simple mate in 1 tactics that just happen to be higher rated.
Are tactical ratings for problems assigned based on the source game? Or are they assigned based on how easily people get it right? It's pretty annoying to have giant point swings after a bunch of +1s.