Beech Super King Air pilot reported diverting to an alternate airport after experiencing engine issues related to low fuel quantity.

Narrative

Prior to departing on a training flight; I requested fuel be put in the airplane. The fuel order was top the main tanks and 30 gallons per side in the auxiliary tanks. I watched the fuel truck pull up to the airplane and set ladders up next to the main tanks. The [worker] came up to my office and asked me to confirm I wanted 30 gallons in the auxiliary tanks. I confirmed that was correct and restated 'mains + 30 a side'. Once seeing the fueler on the ladder I went back to preparing for the flight in the office.Once I got to the airplane I performed a standard preflight which included looking at the fuel gauges. The fuel gauges showed full main tanks and approximately 200 lbs in the auxiliary tanks. I flew the airplane on the training flight and ended up in ZZZ to drop off another pilot to pick up another aircraft which was there for maintenance.I departed ZZZ headed back to ZZZ1. About 20 minutes into the flight; I noticed the fuel gauges were reading empty. Out of an abundance of caution I asked ATC for a deviation to ZZZ2. Shortly after that request the left engine started to roll back. I quickly asked ATC for a closer airport and they suggested ZZZ3. I said I was going to ZZZ3. They gave me a descent and once I had ZZZ3 in sight; I canceled IFR. Shortly after that; the right engine rolled back. I landed without incident and was able to clear the runway.I realized the fuelers only pumped 30 gallons per side into the airplane and did not top the main tanks. I do not know why the fuel gauges showed what they did prior to leaving for the training flight.In the future; the company will implement a policy to stay plane-side while any aircraft fueling is taking place to ensure the proper quantity is loaded. I learned a valuable lesson on this day. I had a rough training event and I should have combined this report with the one I submitted last night. This will NEVER happen to me again.