Their conclusion "the tweeter's step has begun to decay..." is plain wrong, for the reasons mentioned. The assumption that the speaker's main lobe is tilted downward is most probaly invalid. One simply cannot infer such info from a step reponse, you either need to have vertical polars or individual mag/phase responses of the drivers.
The 600 has higher crossover frequency and, more importantly, a supposedly much better designed crossover with steeper slopes. Crossover parts are a big factor for BOM cost, that's why on the very cheap lines designers try to get away with the lowest part count and the cheapest stuff.
A quick sim with for the 600 (assumed flat to +-0.2dB) with 1.5kHz XO and 5th order (acoustically, as always) on the woofer (ported @50Hz) and 4th order on the tweeter (set back by 100us), both drivers in phase, gives the following step response which is not that far off.
In that sim I actually have some 60° phase offset at XO (not a good idea, but used for the sake of demonstration), the tweeter lagging, which makes the main lobe tilt upwards, not downwards, which illustrates the above point.
View attachment 50949
If you look hard, the initial rise of the woofer can still be identified
IMO response of both drivers looked something like this (midwoofer in red, tweeter in blue):