It's not just differences in country but in region... but that is only if you are using dialogue.
I personally think both are acceptable and have heard them used interchangeably by the same person... Technically, I suspect the root here is that 'round' could be a contraction of 'around' and so the correct usage might once have been:
For me it was the other way '
round: I knew things would get better
In many grammar issues, the problem does not so much come in what usage you use but that you are consistant with it. There are many controversies in grammar (which is why it is such a confusing subject) as there are differences in usage in different regions, different styles, etc. It is therefore not a crime to use a perfectly acceptable usage consistantly throughout a piece. It is a crime to use first one usage and then another, even if both are valid.