The situation that you have described is not "USUAL", by which I mean "expectable" or "acceptable". The situation that you have described is rather common, especially when commissioning a turbine driven equipment string, but should be solvable.
The turn-down that you have described - from 1200hp to 950hp is not severe. The turbine and controls should be able to handle this.
There are too many variables that you have not described for anyone to be absolutely certain of the problem based only on your post, but it is a good guess that the control system is not properly functioning at the part-load condition. This is sometimes called "hunting" - the control system is "hunting for the set point". It might be necessary to change the control system settings (proportional range, sensitivity, reset) to try to improve the behavior.
Certain mechanical conditions can also contribute to the problem: loose valve and/or control system linkage, or the governing valve settings are two examples. If the position of one of the governing valves is near to its seat at the part-load, the sensitivity of the entire "turbine system" might be higher at part load than at full load, and thereby make the equipment string more vulnerable to "hunting". Loose linkage is something that, by itself, will not cause hunting, but might contribute to it when it begins. There is likely to be some hysteresis - asymmetry of the oscillations if the linkage is loose.
Control system settings should be reviewed - preferrably with the OEM.
At the part-load point you could try to slightly throttle the steam upstream of the turbine; either at the trip&throttle valve, or farther upstream. DO NOT DISABLE ANY OF THE SAFETY SYSTEMS IN ORDER TO DO THIS. If the steam pressure to the turbine is changed (reduced), the governing valve(s) must move to try to hold the load. If the oscillation is reduced by throttling the inlet steam, the governing valve is "bouncing" around on its seat at unthrottled part-load. Governor valve settings might be modified so as to improve the part-load response.
It is also possible - very unlikely, but possible - that there is some sort of flow oscillation in the process side, and the pump load is actually oscillating. Rule out the turbine control system first. Check turbine mechanical systems next, then look at the process flow.