Be careful if you install over your existing tile, you may not be able to get the dishwasher out if it needs repair or replacement. Also, it will be very difficult to get the refrigerator out if you do not install under it. I had this exact same problem back up north, had to break the glue bonds on the counter top, jack it up to get dishwasher out. This was a wood and laminate counter top, no idea about stone.
Bottom line, make sure you will have clearance for maintenance of appliances, or consider removing the tile.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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