If one were to measure dath ilan's response rate to hallucinations, this would be a very noncentral example of an already usually impressive institution. All of these people are already under redundant observation, and the hallucination handling protocols have been streamlined optimized extensively over the last week. That three people have a severe one at the same time is flagged immediately, and the protocols implemented immediately following. Even now, in a system as efficient as dath ilan's current one at taking in hallucination data, the flow of information is not instantaneous. When the first report reaches exception handling, it is taken seriously, but when the second and third follow shortly afterwards, the importance jumps yet further. It is not impossible that three people would all hallucinate the same event at once, or that this is some trick internal to Civilization, it's pretty flaming unlikely, and their priors for the seventh planet exploding are immensely higher than they were last week. Realistically speaking, this data permits two primary interpretations. One, that the physical laws that embed both their previous model of the universe and it's current state offer magical powers to human minds under some circumstances, or two, that this is a message from aliens. Dath ilan is not so irrational as to fail to realize laws of physics that consider human minds as natural categories are designed, but there is a bit of a difference in actions implied by what degree of remove the other minds are currently at.
In the first possibility, this warning needs to be taken seriously. There's not that much dath ilan can do about it in the grand scheme of things - they are far from possessing the ability to stop any such explosion. Thankfully, they also shouldn't need to; the people involved double check their intuitions against experts, but this confirms their understanding of the situation. Dath ilan's previous model of physics doesn't permit the 7th planet to detonate, nor does it consider it to be especially meaningful if it did, but even in the least convenient world where it was perfectly converted to energy there's limits to the problem. The sun is an immensely larger ball of hydrogen and helium constantly undergoing fusion, and is about 20 times closer; at scales like this, the square cubed law is a bitch. By the time the resulting energy reached dath ilan, it would be a sphere 3 billion kilometers in diameter, with a corresponding surface area of 118 quintillion square kilometers, and the seventh planet is only 100 quadrillion kilograms; the upper bound for energy hitting dath ilan is the equivalent of a day worth of sunshine, and their 90th percentile guess is orders of magnitude lower. It might still do any damage, but the direct impact is not the priority; a lot of their possible actions are covered under what they're already doing, or will be with some minor re-prioritization. The possibility is, however, still absolutely flaming terrifying; dath ilan would prefer its planet unexploded, and indeed otherwise relatively intact, thank you very much. With the expected payout this high, dath ilan also steps up its effort to induce the headaches and hallucinations. Even if they are just informational sources, that possesses immense value in itself, and if they have some effect on the causation of what they see that provides a potential path to the actual survival of dath ilan. Fortunately, many of the keepers are experiencing these headaches, but dath ilan does not try one obvious thing and then stop; also brought in are artists, mathematicians, programmers, authors, as well as assortments of other populations in smaller numbers. They start with trying to effect a few small asteroids easily observable from dath ilan; if this actually is a type of economicmagic that operates on the scales of planetary destruction, dath ilan does not exactly want its first, least controlled usage to be taken in the same place they keep all their people. By the same logic, searches are conducted among dath ilan's populace, especially those comatose or hallucinating prior to the advent, in case the event is being caused by one of them. It's an obvious hypothesis, if you're entertaining the idea that minds can warp the physical world at this scale.
The second, that this is a communication, seems both more likely and with higher median payout if true. Dath ilan has been broadcasting information, first contact protocols, and requests for aid already, but they update some of those to acknowledge the message. Other, more speculative methods of communication, like speaking directly to those most effected or asking people suffering from the headaches to try and think back responses, are both deemed worth trying currently. If this is true, they should not only be taking the actions listed higher up, but also create a more direct line of information flow between those most seriously suffering headaches and hallucinations to the people organizing dath ilan's disaster preparations and first contact groups, as well as arrange exception handling to more efficiently funnel such results from the rest of the population as needed. These actions would also be sensible in the case of the hallucinators possessing some kind of distance-datacollection-economicmagic-capabilities (a 1 syllable word in Aeldari), but take on additional value under the latter hypothesis. Dath ilan does not dismiss the possibility of the hallucinations being aimed to redirect their efforts in a way advantageous to some adversary like some on earth would, but neither does it obsess over the possibility like others might. They consider their estimates for cost versus value to potential agents across different capability spreads and find it in expectation unfavorable, particularly given that most of their wide scale emergency measures are only minorly altered and they don't seem to have anything meaningful in the way of options for altering attack surfaces on their leadership to whatever is causing the headaches anyway. A 4th rank keeper is assigned to keep track of the evidence to make a decision on if that changes. Obviously there are others who will do that, but they are the one person whose job that is; dath ilan believes in making a specific person responsible for things that absolutely need to happen.
Astronomers divert more of their attention to watching the seventh planet. If it does explode, they expect they'll notice regardless, but they would definitely prefer to watch the leadup and see it happen. Attention is paid to how much time passes between the hallucinations and the explosion becoming predictable, if it does; such information would be useful in determining where in the causal leadup the information they received is coming from.