really wet mob ruins the tiles, but if u dry very well and than use it will not. i use the following bucket to dry:
http://www.bestlight.com.au/smoothgallery_2/images/portfolio/squeeze_mop_bucket.jpg
it also depends on ur mop too. get good qulity one…i usually buy from bunnings, they are heavy and stong but really good
steamer is really good with all the grout and spill and u dont have scrub with it.