There is a special setting on the water level control, lower than minimum and usually at the bottom of the dial.  You can barely see the 'mini wash' setting on the far right of the dial on the GE washer in today's POD. 

I remember the 70s machines I had owned which had the mini basket, there was a distinct 'click' as you turned the water selection to the mini wash setting.  I guess because between Low and High, the control allowed for infinite settings. 

The mini-basket was introduced in '62, IIRC.  I briefly owned a 63 GE with the mini wash setting, but no mini basket!  

The Mini-Basket was introduced in 1962 and was included in their top two models for several years until it became popular enough that they spread it out even into a couple BOL models. GE had a huge range of models to choose from each year, second only to Sears, I believe.

The GE mini-baskets were filled, via the Filter flume, by the same pressure switch that was used for the regular washbasket; the Mini machines simply had a fourth extra-low setting that I still find quite handy when washing things like rags where, instead of using the mini-basket, I'll go against posted instructions and let the rags get agitated in the big tub. I still find the mini-basket very handy when I need to wash stuff like gym shorts, napkins, guests towels and other tiny loads that would either take forever in the Miele or would just sit in the bottom of the tub in the 1-18. It must have been popular because it lasted for 3 decades despite the pissy criticisms of Consumer Reports techs who thought the Maytag A606 the acme of automatic washers.

The system for filling the Hotpoint mini-basket on its short-lived Duo-Load models was much more complicated than GE's. It combined the timer, a special lid over the agitator and small tub that looked like a GE filter-pan but had special float valves to make sure the water inside the small tub never mixed with the water in the large tub (during the wash; the waters eventually met and mixed in the outer tub during the spins) and a special fill flume.

Short version: when the machine was energized the washer filled the mini-tub first and then, when the timer determined that the small tub was full, the temperature of the water would change ( if the user so desired) and, simultaneously, the lid float valves would close and the water would overflow into special channels that would divert it into the large tub with the remaining fill water. Very tricky for a pre-computer-controlled machine without a pressure fill switch (Hotpoint might have changed that for the second model year; I can't remember).  CU crucified this machine; very bottom of the ratings. It had lots of issues besides the whole Duo-Load chazerei but they at least allowed that the Hotpoint Mini-tub system was more capacious and more efficient with water usage than the GE's.

I still comb the auction sites for a Duo-Load; I think it must be one of the rarest automatics ever built.