B737 Captain reported uncommanded fuel transfer during cruise. Tank 1 was transferring fuel into the center tank. The crew ran the fuel balance checklist and were able to continue to their destination.

Narrative

At cruise altitude when the center tank fuel quantity indicated zero I positioned the center tank pump switches off and a fuel imbalance was noticed. It appeared that main tank 1 was transferring fuel into the center tank. The fuel IMBALANCE non normal checklist was initiated. Per the checklist with the cross feed valve open; center tank pump switches off and the main tank 1 fuel pump switches (both) selected off fuel continued to transfer from main tank 1 to the center tank. An imbalance of approximately 2100 pounds was noted. Not wanting the imbalance to get worse I reconfigured the fuel panel to its normal position to stop the transfer. A phone patch to Dispatch and Maintenance Control was initiated. It was determined that we may be experiencing an un-commanded fuel transfer. I was only able to balance the fuel by completing the fuel imbalance checklist with fuel in the center tank and keeping the center pump switches on. If the checklist was followed (center pumps off) the main tank 1 would start transferring fuel to the center tank. We landed in ZZZ1 uneventfully and taxied to the gate. After landing I turned the center tank pump switches off with the center tank indicating empty the attached fuel imbalance occurred in approximately 13 minutes.