Cheap load cell and ADS1232 strange oscillation
This may very well be a thermal stabilization of the strain gauges in the load cells as the excitation gets applied. Since you have four devices in parallel there may even be a difference of stabilization characteristics between them that makes this problem more apparent.

I can suggest an experiment to help isolate if what I suggested above is true or not. Try leaving the excitation on to the load cell strain gauges all the time and then just turn on the electronics subsystem. If the problem does not re-occur then you know it is the load cells stabilization. 

On the other hand you could run a second experiment where you leave the electronics powered all the time and then just switch on the load cell excitation. This will give you some additional data.

Lastly I would suggest running an experiment where you just run one load cell and see if you see the problem in this single condition. If a single unit behaves nicely then you know it is the parallel combination effect.