I have seen this too. I believe as posted above it relates to page size and using 100%. I noticed certain browsers open a border container pane wider or narrower which affects the size of the 'map' object in the center border container pane, at least if it has a splitter and is set to percentage as mine is. It seems slightly differently sized in each browser, I will check this some point soon and report back...
It is unfortunate, I wish there were a solution. What it basically means is you're never sure the EXACT extent if you have users with differing monitor resolutions and browsers. I am going to have to just explain that to end users. They wanted the "same" zoom and extent for all situations and when you have tiles it doesn't seem possible, it jumps a bit to one direction based on size of the map. Only way would be to lock down the size of the viewport of the bordercontainer pane containing the 'map' object, that I can think of..