Yes, those multimeters have a 6th sense, they provide a tingling sensation when mains voltage is measured. However, with a CDI circuit, both you and the multimeter give out sparks. Not trying to bring down those cheap meters, they work GREAT (when probes are not oxidized and make contact), are precise (after calibration), safe (at low voltages) and repeatable (with a fully charged battery).
I would just treat any of those meters as disposable, since they cost <20$, and count myself lucky if I'm not getting a shock. Any half-decent multimeter should survive 1500V. However I haven't seen anyone test them for 20kV. I don't think any professional puts 20kV on the probes, but beginners are likely to do that. So I would add that to the range of multimeter tests, in addition to 'ohms-range on mains voltage'.