The ETCCDI is rather picky about percentiles. According to them (as per implementation in reference code), the method to calculate the percentile should be Hyndman & Fan method #8 . This is also the preferred method by NIST. This method is available in the R package, although not as default, and in scipy.stats.mstats.mquantiles.
The method is however not available in numpy.percentile, and there seems to be some confusion regarding methods and their implementation. In particular there is an outline for a numpy implementation of all H&F methods in this comment, but it seems that progress on this has stalled.
Moreover, the python percentile calculation 'ecosystem' becomes more diverse with a Python3.8 percentile function.
The Iris percentile function is divided (depending on arguments) into a fast method (cf. Iris issue #3294) using numpy.percentile, and a normal method using scipy.stats.mstats.mquantiles with default **kwargs corresponding to method H&F#7. However, according to the Iris documentation it seems that main distinction between the fast and the normal method is that the former does not handle masked data and the latter does. The fact that the normal method have all (continuous) H&F methods implemented is not well documented.
 Hyndman, R.J.; Fan, Y., 1996. American Statistician, 50 (4): 361–365. doi:10.2307/2684934. JSTOR 2684934.