Hi, this isn't surprising, unfortunately. :( I'm sorry.
Soap is not usually a good choice for sensitive, Rosacea skin - it's drying, and has a very high pH that further imbalances the . And Seabuckthorn has not been shown to be particularly useful, despite internet claims.
Also, Demodex mites may not have anything to do with your symptoms (I'd go so far as to say: it's highly unlikely). There is a condition resembling inflammatory, papulopustular Rosacea that is linked to Demodex infestation, but current research does not seem to connect most Rosacea cases with Demodicosis.
From Facedoctor website:
The active ingredient, Seabuckthorn Oil, is clinically proven to kill the Human Demodex parasite. Cleansing effects of rosacea.
One bar lasts 3-4 months.
Made from natural plant extracts that were developed to deal with the causes of ugly skin such as redness, enlarged pores, acne, skin blotches, rosacea and premature aging.
Neat Soap Flakes, Seabuckthorn (hippophae rhamnoides) oil, coconut oil, aloe barbadensis (aloe vera), glycerin, sodium silicate, astragalus membranaceus, spirodela polyrrhiza, tocopherol (vitamin E), protein hydrolysate, fragrance.
I don't mean to hijack your discussion, but these products have been mentioned by several members recently, and I see these ingredients and just grit my teeth. So, please know this is not directed towards you specifically.

The following may be a slight rant, and I have removed my Moderator's Cap for the duration of this post.

There is no clinical research regarding claims Seabuckthorn Oil treats Demodex and Rosacea. Period. There are many claims by websites and companies SELLING Seabuckthorn oil products. Seabuckthorn may in fact have some lovely qualities (it's high in anti-oxidants, for one), but nothing but nothing is a Holy-Grail-Cure-All. I like Seabuckthorn Oil, I use it in skincare, it's a very nice botanical oil - it has not cured my Rosacea. It has not worsened my symptoms, it also has not cleared them. That doesn't mean it won't help someone else's - but like almost everything out there, it's not The Answer For Rosacea. Anyone who tells you they have 'the cure', and they would be willing to sell it to you ($20 for a bar of soap? Really?) over the internet, is just selling something. Please don't put your faith, hard-earned money, and health in the hands of someone who just wants to sell you something.
Soap, in general, is hard on your skin. The ingredient here is 'neat soap flakes' - this tells us nothing. Is this true soap, resulting from a chemical reaction between oil and lye, leaving a product that is highly alkaline in pH, and probably very drying to your skin? Is this a detergent or emulsifier instead? Which one? There are MANY. They don't tell us, so we really have no idea what the most basic ingredient in this product is - and what it will do to skin that is already sensitive. Will some people be able to use this and benefit? Probably. And that is due to the combination of ingredients working for them - and probably other factors we won't ever know about. Aside from the 'soap flakes', the rest of the ingredients are perfectly fine for anyone who is not sensitive to them. They are not, however, ingredients with any proven action against Demodex mites, if that is truly an issue. This is just soap. The way soap works, the ingredients in this are unlikely (I say with great understatement) to have any effect on your skin whatsoever. In a creamy, non-bar-soap, mild cleansing base, the Seabuckthorn Oil, Coconut Oil, Aloe Vera, Glycerin, Astralagus, and so forth might actually do something for your skin - especially if it was a non-stripping, creamy base that sat on your skin for a long time (think hours) - but as a drying soap that you lather up and rinse off, all you are doing is stripping away more and more of your natural protective skin barrier and leaving nothing helpful in its place.
So, this is soap. I don't care what kind of amazing, Holy Grail, Cure-All, exotic ingredient is added to soap - it's still soap. Soap weakens the skin barrier. Period. Healthier skin will recover quickly. Sensitive, Rosacea skin probably will not.
If you would like to try Seabuckthorn without the irritating soap factor, there are a lot of online sources for the oil (oil from the fruit/berry has a strong orange/red color that can stain skin because of its higher lycopene content, oil from the seed is lighter & non-staining - I believe they have similar constituents, aside from lycopene levels).
OK, rant over. Good luck everybody. Keep it simple, keep it gentle.