Percentile function uses some sort of an interpolation at some point, e.g. see NIST handbook. this will lead to a different answer depending on whether you took the logarithm before or after applying percentiles.
If you were obtaining the percentiles analytically then the order of operations wouldn't matter because Log is a monotonic function. you could get the percentiles on original variable, then get the log of the percentiles. Alternatively, you could first transform the variable, then get the percentiles. both would render the same answer analytically, but when you do it from the empirical dataset the results are different.