Time taken by power supply to reach output voltage
this catalog has more info for the Keithley stuff, for the 2260 they do not have actual response times for commands, but mostly how long it takes the unit to change or recover from different load situations. Rise or fall, etc. Seems under 50ms is typical.

The 2600 series seems to be at the speed range you mentioned, you can search for COMMAND PROCESSING TIME in the document and see for yourself they state under 1ms for commands there.

other models have under 10ms.

http://lmnov.ru/upload/eng/Keithley_2014_eng.pdf