Q: Is it important what I clean my dissipative work surface with?
A: Yes.
Would you want to clean a PCB with something like Jif or glass with shampoo? They may do something of a job, but they're not appropriate.
Static dissipative / "antistatic" / ESD bench mats all need to be cleaned with an appropriate cleaning solution.
Many cleaners, including some "antistatic" cleaners, contain silicon & other contaminates that can either coat the surface of your mat with an insulating layer ... rendering them out-of-spec' ... or transfer contaminates to your product with unwanted results.
Case Study here:
One of our clients bought some WorkStation Kits… after a few months, we were approached with the concern that the resistance values of the dissipative bench mats were getting high, to the point of 'failing' the path-to-ground testing. On further investigation, it was discovered that various chemicals were being used to clean the bench mats… including a can of "antistatic" spray foam. The bench mats are not "antistatic", they are "dissipative"; 2 very different properties that require different cleaning regimes. Once the mats were thoroughly cleaned back to the original surface & regular cleaning with ICSC was implemented, the bench mats returned to their original resistance range, which is well below the 1 x 109Ω RG (Path-to-Ground) limit as specified in IEC61340-5 & ANSI/ESD S20.20.