Pufferfish are sea fish, not desert fish so unless you have a mod that changes locations it’s no surprise you couldn’t catch any in the desert.
If by advanced iridium rod you mean the vanilla game one Willy sells, that has no influence on the fish quality. Fish quality is determined by distance to shore, your level and a random factor. You can only get iridium by making perfect catches or using a quality bobber.
Did you catch iridium fish with the fibreglass rod? Which mods do you have?
That's... really weird... I swear to god I've caught them in the desert before. Either way, no, I'm not talking about the one Willy sells, I mean the Advanced Iridium Rod that you get from the Cave of Mastery. I tested it out just now, and I was able to catch an iridium woodskip on my farm just fine, but the sandfish and scorpion carps in the desert don't have any stars on them, no matter how perfect the catch is.
I have about 29 mods in total, most of which just change aesthetic stuff in the game or add certain events to it. I've got CBJ cheats installed which you can use to just always get perfect catches, but considering that it seems to only be the desert fish that are effected right now, I'm not entirely sure how it would glitch like that.