Well Pix’s answer is the simplest.
We have to keep in mind that for MS in UL there is not difference in Transmitting on SD and similarly no diference in receiving in DL. The MS takes info of MAL / MAIO and TS to evaluate which frequency to transmit / Listen.
For SFH Its easy to visualize as radio changes frequency for all TX every frame. so it changes the frequency for SD on it as well.
In BBH:: The baseband signal fed to the radios(each transmitting at fixed frequency) is changed. so the radio only acts as a RF modulator. and on the base band both the TCH and the SD are a set of BITS. so (Bits of ) SDCCH are shifted between radios in the same manner as the (Bits of) TCH are shifted