"Why wouldn't you travel by main roads?"

Episode 4, Of Banquets Bastards and Burials - Jaskier

So, while Geralt and Jaskier interact quite a lot this episode, I'm going to do my best at separating the two metas because there's also a lot going on and believe it or not, I think it's even harder to follow swinging back and forth between Geralt's view of the situation and Jaskier's than just talking about them in parallel like this.

And, for reasons that'll be a lot more obvious on Geralt's meta, I think it's best to do Jaskier first and lay out how he sees the situation.

Man: "And he stood in the middle of that frozen lake like he knew it was coming for him. The ice cracked open and a selkiemore shot out! Oh, you've never seen one, but it'd take down a ship with its cavernous mouth full of devil's teeth! And it... swallowed... that witcher... whole!"
Jaskier: "Oh, this is brilliant! Oh, sorry. It's just Geralt's usually so stingy with the details."

Something to note here is that Jaskier does not appear to follow Geralt onto the field. He generally or always gets his information from Geralt afterward. And in this instance we know Geralt didn't insist on going alone given this other man was there and saw the whole thing himself, so that would appear to be a choice Jaskier's making.

Now, there may, admittedly, be extenuating circumstances. For one thing, it's snowing and the man mentioned a "frozen lake". Jaskier may have decided that comfort is the better part of valor and stayed indoors. It's also possible that Jaskier only just arrived and it's just a happy accident it happened when Geralt was mid-job. But he doesn't appear to be lamenting that he missed his chance to see it with his own eyes and "usually" sure sounds like he also usually gets his information from Geralt, rather than first-hand, even though he "usually" finds Geralt's version of events lacking. I don't think he's actually following Geralt on jobs much, if ever.

(It's not impossible Jaskier screwed around too much and Geralt decided Jaskier in particular wasn't allowed to come with him on jobs - but it seems unlikely Geralt could enforce such a boundary on Jaskier given how emphatically he failed at that in their first meeting, and even more unlikely that Jaskier wouldn't be complaining specifically about that. We also, as I got into in the second episode, don't see any evidence for Jaskier actually foolhardy and wanting to regularly risk himself.)

There is a second bit we can interpret: "so stingy with the details"

While the most likely way to take this is that Geralt just does not give enough details for Jaskier's taste, it could also mean Jaskier does get them, he just has to pry them out with question after question instead of it being volunteered in full without prompting, the way the man here is talking.

Jaskier: "Uh... and then what happened?"
Man: "He died."
Jaskier: "Eh... He's fine."

This is funny, but I think it's also noteworthy in the question of does Jaskier develop over the course of the season.

We know in his first appearance, he cheerily follows Geralt into danger while talking loudly. Even tied up he assumes there's nothing to worry about. Does he understand now that Geralt can't necessarily keep him safe under every possible circumstance? Presumably given he's fine getting his information secondhand either most or all of the time. Does he still believe Geralt himself is an unstoppable badass who can't die? Absolutely. This may be coming from a slightly more reasoned place than before, since he knows a lot of what Geralt's accomplished and that the guy's still standing, but it's still the same attitude.

It's also worth considering what this means about the common assumption that Jaskier is seeing the rough bits of being a witcher and helping out. This is not a Jaskier who's ever had to find Geralt after he's collapsed too injured to return to the inn. It's not even a Jaskier who's had to sew up Geralt's injuries or seen him in pain, because to talk like this knowing Geralt could be that hurt would be callous.