With the Tiger Cloth, I have made a recent discovery that is not a concern, but as it is inquired about, it may be relevant.
The Tiger Cloth has now been used as Neil Described on approx' 70ish Albums. The DIW Rinse is carried out with Pressurised Bottle with a Jet Nozzle, it does work sufficiently as a Blast Rinse.
I too leave the T'cloth out to air dry and then in a sealed bag to store it.
Recently I purchased a Camera Lens that I have put through the wringer of learning its qualities over the past few months and only a few days ago decided to give the Front Protection Filter a Clean. My thoughts went to the Tiger Cloth which I utilised.
The cleaning was not successful for the Lens with the Tiger Cloth, as there was a new produced smearing showing on the lens filter that was remaining. I had to use my usual method that is a Lens Fluid Cleaner and Lint Free Paper Towels to clean the Lens to the standard usually achieved.
As said, this is not a concern, as I genuinely don't see the T'cloth as causing any cleaning issues with the Vinyl Lp's, it is very efficient at absorbing the thin film of DIW following a rinse and Sponging Dry.
What the T'cloth is most likely also collecting, is a very miniscule quantity of a Solution, and after 70ish uses has enough contained in the proportion of the Cloth I used on the Lens to be detected on the Glass.
Prior to using the T'cloth on a Lens in the future, I will soak it overnight in a distilled water and when dry, try it on a Lens to see if the smearing has ceased from occurring.