With so many variations of rounding, the "right way" of performing the operation appears to me a moot point.
For example, using the 1.1875V value displayed on your Fluke, I was taught in chemistry that if the least significant digit is 5 and the next decimal over was unknown, then rounding to 4 significant digits would yield 1.187V, justified by uncertainty in 5. In contrast, if the meter read 1.18750V, then this value would be rounded to 1.188V since the uncertainty lies in 0. By this convention, even Fluke's algorithm is "wrong," so to speak. That is to say, what makes floor(x) "wrong" and ceil(x) "right" beyond arbitrary convention?