EXACTLY. Mine does this; after long motoring runs, I get warm water out of the cold side spigots.The pump is on both sides. Feeding cold and heater simultaneously. Otherwise one side would get no input pressure.
When the heater pressurizes with heat, especially from the motor, hot water can travel backwards to the cold side when a valve (faucet) is opened, without ever touching the pump, which may have its own check valve or enough resistance to cause the hot water to take the path of least resistance: the open faucet.
Mine did this years ago. Troubleshooting found the bronze check valve stuck slightly open.