Can this be used on a roof deck that is finished with a rubber membrane? Will the deck tiles puncture this membrane?

Yes, although the chance of puncturing is low, you may want to place an additional TPO or EPDM membrane / polysheet above your existing rubber membrane to avoid any damage during the installation process. We recommend a minimum thickness of 40 mils. We do not have a recommended product or manufacturer. The deck tiles themselves do not have any sharp points on the bottom.