One of the things to remember about part-worth utilities is that they are estimates, not exact "true" points. There is a range of uncertainty surrounding each one. We can compute a standard error (the standard deviation divided by the square root of the sample size) and then multiply the standard error by +/- 1.96 to obtain a 95% confidence interval. We are 95% confident that the true utility falls within that range.
My guess is the change in preference order you saw for levels within an attribute when comparing zero-centered diffs to raw utilities did not represent a statistically meaningful change in preference. But, you could compute the 95% confidence intervals for either (or both) of the raw utilities or the zero-centered diffs to see if the 95% confidence intervals overlapped for those two levels that traded places.
Zero-centered diffs does a better job more equally weighting respondents than raw utilities, where some respondents (the most clean and certain ones) can have a larger weight in influencing the mean utilities.
The interpretation of the utilities follows the same rules. Zero-centered diffs are just placed on a bigger scale. The overall magnitude of the scale does not change your interpretation of the part-worth utilities. You could multiply all the part-worth utilities by 2 or 100 or 1000 and your conclusions should not change.