When you cleaned the camera lens did you use the tiger-cloth dry, or did you use your lens cleaning solution and try to dry with the tiger-cloth?
When you use sponge & tiger-cloth for record drying, do you wear gloves?
What specific sponge are you using? How do you get the water out of the sponge after use and how do you store it?
In between cleaning steps, do you rinse/dry your free-hand (that works the brush) a little which will pick up some cleaning agent? I have a lint-free microfiber cloth that I hang and grab it with my free-hand to somewhat dry it between steps to minimize cleaner carryover noting that when I go to dry with the sponge, it's the same free hand that was working the brush with the cleaners.
The tiger-cloth is not very absorbent - so if used with a lens cleaning solution, it may not remove the lens cleaning solution enough to prevent leaving a residue. If used dry it could just smear what was on the lens.
Again, for record drying, the tiger-cloth is not used to dry the record. Instead, it takes the water left behind by the PVA sponge and absorbs some (but not much), but mostly it spread outs the water to a thin uniform film which then dries quickly. Otherwise, water droplets can take over an hour to dry.
After cleaning six records - my PVA sponge is very wet (I just ring-it out) but the Tiger-cloth is barely damp.
In the meantime, I have used the same tiger-cloth as I address in the book over 500-times w/o problems. Any haze is readily evident on the lead-in groove and the dead-wax (run-out) areas. I have contaminated a PVA sponge and the haze was evident - I tossed it (reproposed for floor cleaning) and got a new one.