Chessex recommend these Staedtler brand markers for their vinyl mats as they are designed for plastic.
It is recommended to first test any new pen on a small area such as the border, and wait at least 30 minutes before wiping off to insure that colour wipes off properly. Often the colours that stain are not constant due to small changes in the manufacturing of the markers, so it is good to do this test whenever you get a new pen. Please note that red markers from any manufacturer tend to stain quicker than other colors, so use sparingly and mainly for highlighting. This applies to the red pen included in this Staedtler 4-pack.