I have observed over the years that grease separation in automated system lines can occur when the line size of the main header is sized to large. During the cycle of pressurizing and venting to operate the metering injectors, over time this action can start to squeeze out the oil from the carrying agent. This usually happen with greases of lesser quality or the occational bad batch.
If you have it happening at 30-35 psi on your pump, and assuming it is a 50:1 unit, you are only seeing approximately 1500 psi on your grease system. This usually happens at pressures over 2500 psi and at high cycle rates of say more than 4-6 cycles a minute for extended run times of hours on end. You also have the issue of trying to pump the left over thickener through the lines and metering units which just isn't going to happen at those low pressures.
If it was vibration it would also show up in the drum, in any case I would follow Bruce's suggestion and change grease.