Then you did nothing as top:0 is the default . The element would not have been moved at all and would look the same everywhere. Relative positioning should not be used to move structural stuff around anyway as it does not move things physically only visually. It is used for more subtle overlapping effects instead.
If you have moved many things using relative positioning then that is likely the problem because nothing will appear to be where it should be and there will be various gaps in the page.
Perhaps you meant absolute positioning but again all browsers will treat that exactly the same if you have implemented it correctly. Chrome and Safari essentially use webkit but chrome uses a fork of webkit called blink which has some differences although none of which will cause your problem.
I can guarantee that the issue will be with your coding rather than any specific browser differences and messing around with percentages isn't likely to yield any positive results (why should it). (Positioning with percentages sounds a very doubtful approach to me unless its something in a very controlled situation).
Basically you need to find the error in the logic of your code.
What is the current stacking context for the positioned element. Have you taken account of default margins/padding and cleared floats correctly. Is the code valid have you run it through the validator.
Are you trying to move something based on the expected height of something else.
Just to re-iterate absolute and relative positioning work in exactly the same way in all modern browsers (excluding obvious bugs) so it is likely something that you have set up wrong or incorrectly along the way and confused the browser.
Without a demo or test then its hard to give specific advice but I can tell you that the differences that you mention can usually be solved in seconds with access to the page in question. If you can't supply a url or a demo of the problem then it will be hard to give specific advice. Perhaps you can post the code for your positioned elements and structure so we can get a grasp of what you are doing?
Having said all that then yes browsers do have bugs and indeed you may have tripped one but 9 times out of 10 it will be the author at fault rather than the browser:)