A couple of thoughts here.
OP's basic problem is a cheap, inaccurate meter, not really whether its true RMS or not, although true RMS would more likely show up on a decent meter.
Decent meters without true RMS are usually made to show the RMS value of a sine wave at mains frequency (50-60Hz), and should say so. Mains voltage is really close to a sine wave. Today it is cheap to produce a digital meter with pretty accurate DC and true RMS AC, but only up to typically 400Hz. It costs real money to get really good DC and AC accuracy (say, less than 1%) and good frequency response for AC measurements. Some people will look at a meter's specs and see that it measures frequency to maybe 1MHz, but this always refers to the frequency COUNTING function, not the AC measurement range.
Cheap meters can sometimes be OK for low voltage DC and ohms tests, but their typical failing is safety. There is a lot of energy available when testing mains (in any country). All it takes is a mistouched probe, mistakenly setting the meter to ohms, or a meter with a design inadequate for mains voltages and you could have a meter literally explode in a ball of flame in your hand. A good meter is designed to minimize the danger, but apparently some vendors choose to be dishonest in marking their safety ratings. That said, I did try a free Harbor Freight DMM in my mains (carefully) and found the reading wildly off compared to my Fluke, Brymen and even a Kill-A-Watt.
There's lots of interesting chat on meters in the nice Aussie EEVBlog site:
http://www.eevblog.com/forum/testgear/
Fluke makes great kit, but they do have products that may not be appropriate for your use. Only their most expensive handheld meters have AC response up to 100kHz, so anything else may not work well if you need to measure AC and harmonics like that. But I think every Fluke should measure mains voltage accurately.
The link about true RMS not being good only shows the difficulty of calculating accurate AC measurements - it's much harder than DC. And users don't usually have options to turn true RMS off. As always, the user should know what they are doing and the limitations of their equipment. DMM specs are trickier than most would believe, especially regarding AC.
I'm not sure about measurements of your stator generator. It may be DC, but pulsed according to RPM and really AC+DC unless filtered and smoothed. That's another measurement problem.