The linked article talks about the effects of caffeine on the brain, including the brain fog that can come from drinking too much of it. This is technically true, though not directly. The article linked Vail Health's article on brain fog, which states that brain fog could be caused by something "as simple as not sleeping well, or as serious as low or high blood sugar in a person with diabetes." Lack of good sleep can be caused by ingesting caffeine, so to say that caffeine causes brain fog is not wrong, though it eliminates the other factors that effect the brain's ability to focus.
The writer of the original Live Strong article is a full time professional journalist who has a college education at the University of Maryland. The reviewer of the article is a registered dietition with experience in this topic. Both of these people seem qualified to speak on this topic, which aids in the articles credibility and reliability. Both sources that they cite (Vail Health and the Cleveland Clinic) are .org websites, which points to the fact that they're reliable, as well. In addition, other journalists/articles agree that, based on what we know, caffeine causes dehydration and sleepiness, which causes brain fog.
Though caffeine doesn't directly cause brain fog, it causes sleeplessness and dehydration, which is what causes brain fog. Drinking large amounts of Celsius would give a person brain fog because it would cause dehydration and limit their ability to sleep properly, which are both large factors in the creation of brain fog. And while not all brain fog can be linked to caffeine, there's a good chance that caffeine usage will indirectly cause brain fog.