C680 Captain reported asking FBO Ground Service to add engine oil to both engines prior to departure. It was later reported that the engine oil caps were found to be not installed; with oil leaking from the cowls.

Narrative

On Date; I completed a revenue flight from ZZZ1 to ZZZ. Upon arrival; we advised line service that we needed a lav service and if possible; an oil service. I advised the lineman to check the sight gauges and bring both engines up to half on the sight gauges. I went back inside the airplane and began to get the cockpit ready for the next leg to ZZZ2. While I was performing my cockpit checks; a lineman entered the airplane and asked about the oil service. I again asked that if they had time to; to please bring both engines up to the half way mark on the oil sight gauges. I told him not to worry about it if they couldn't do it. On a side note; I had just checked both engines in ZZZ1 and both engines were showing that they had oil in the sight gauges. Both sides were showing at around the 1/3 mark. I simply wanted to add a little to both sides because I knew we were handing off the airplane to another crew in ZZZ2 for a pax trip and wanted to save them some time. After the lineman left; I went back to getting the cockpit ready to go. Once I completed the cockpit checks and setup; I went back into the cabin and noticed that service hub was working hard to get our cabin in tip top shape for the next revenue flight. As they finished up; I went out and performed a walk around. All doors were closed and all locks were secured. We then departed for ZZZ2. Upon arrival in ZZZ2; we took 150 gallons of fuel and then shut the airplane down and went to the hotel. I received a call from the PIC that took over our plane and he advised me that both engine oil caps were found to be off and hanging by the fill tubes and that there were small drip markings on the ground under the drain masts. I advised him that at the time that we shut the plane down; there was no oil found on the ground. It must have started to collect inside the cowling after shut down and taken a while to start dripping out. It's obvious that an oil service was done in ZZZ. It's also obvious that whoever did it also didn't secure the oil caps properly. The issue is that I never even knew we received the service. At no time did anyone come back into the airplane to grab one of us to check the caps. With everything else going on at the time; I didn't even think twice about the oil service. Like I said; the airplane had plenty of oil and this was just to top it off so to speak so there wasn't a dire need.While I ultimately take full responsibility for what happened; I think it's clear that all FBOs; not just Company ZZZ; should have SOPs in place to make sure that at least one pilot is asked to double check the caps before closing that access doors. Had whoever done our oil service come up and asked us to check the caps; this wouldn't have happened. This was a good example of how things can happen outside the airplane while neither pilot has any idea that it's being done. The oil fill access doors were closed. There was no reason for me to assume that anyone was back there servicing the engines while we were inside the airplane.