Why didn't winning Jumanji fix time like in the first film

The only way I see for the two films to have the same time travel rules is if after the end of the first film Judy and Peter get replaced by the versions of themselves that played Jumanji (which obviously we never saw).

Looking at just the first one it appeared that finishing the game created an alternate timeline where Alan and Sarah had the memory of living until the end of the game, in which Judy and Peter never play Jumanji. This alternate Judy and Peter get replaced by the prime Judy and Peter at the time when they entered the game in the prime timeline (after the end of the film).

The sequel seems similar from the point of view of Alex, and it appears that the 2016 group replaced their alternate selves that grew up in the universe where Alex never went missing (who wouldn't have known about freak house). The difference between the two 2016 groups could be a lot smaller than the alternate and prime Judy and Peter, since it appears that Alan and Sarah are going to save their parents, thus preventing them from moving to Alan's house and playing Jumanji.

Temporal mechanics is an enormously complex subject due to the infinite interrelationships between each object in a temporal continuum. Devices and beings that can manipulate time and the fabric of reality may also further interact with objects (or subjects, in the case of the players of Jumanji). Even so, there is a significant difference in how time plays out after the game is completed for Alex, in 1996, than it did for Alan and Sarah, in 1969, as well as in the very fabric of reality that each set of players (Alan, Sarah, Judy and Peter from 1969 to 1995, and Alex, Spencer, Martha, Bethany and Fridge from 1996 to 2016) interacted with each other.

Assuming that winning the game, no matter how long after it started, resets the timeline for all players, we know (from Jumanji: Welcome to the Jungle) that Alan was sucked into a jungle within the game, while Sarah continued to live in the real world (cinematically). Peter and Judy joined the game and, by virtue of rolling a "5", drew Alan out of the jungle, a fabric of reality provided by the game. This is also where all the animals, the monsoon and Van Pelt originated, being pulled into the real world from the game's reality. Once the game was won, and time was reset, Judy and Peter would never be able to remember what happened because the temporal mechanics removed their participation from Alan's and Sarah's real timeline; they all played the game in Alan's and Sarah's reality but in a timeline that no longer existed. Therefore, while Alan and Sarah, as originators of the alternate timeline, could remember, Judy and Peter would not remember, as time was reset before they would have played the game (and, in fact, before they were born). This is what also allowed Alan and Sarah to purposefully interrupt Judy's and Peter's timeline and sparing their parents with no consequences to themselves.

In contrast, Alex, in 1996, and the rest of the players, in 2016, were pulled into the game's reality from their own; everything that occurred was not in a separate timeline, but in a separate reality provided by the game. Upon winning the game and shouting its name, they were each pulled out of the game's reality and deposited back to their own timeline, memories intact. Alex, in 1996, allowed his timeline to play out, choosing not to prevent his future compatriots from playing the game (and who knows if that may have had disastrous results; he may have returned to the game to be stuck forever, or he might have created the dreaded time paradox).

This is answered by Jake Kasdan himself, from collider

“Robin and Bonnie's characters remember it because they're the ones who emerged with the memory intact. And the way that the first movie ends, because they have emerged at the time that they entered the game, the way we've tried it, the way we've sort of played the role also, right? Which is like, you come back out at the time that you went in. They are able to preemptively prevent the kids from having that experience in the first movie. Do you see what I'm saying? So the kids show up in town at the end of the first movie, they recognize them, and there's the scene where they tell the parents, ‘Don't go on a ski trip.’ There's this moment at the very end where they alter the course of the present day in the original Jumanji, 1996 right? And prevent the kids from ever having the experience of playing the game.”

So it's more like if they want to change the timeline or not if the person in past didn't change it everyone remembers playing the game.