Are you using an OEM ECU, or an aftermarket Holley, etc? I am not a tuner of LS engines, so I can't guide you on what scan tool/computer software to use. But I would invest in one so you can check things like this yourself. I can't speak for what your tuner saw on his software. I'd call him and confirm or find a new tuner....you need to see what temp the ECU is looking for when opening the fans. Seeing that you have an LS, the ECU will be relying on a temp sensor located on the driver side head. Unfortunately, an infrared gun on a hose will not match the temperature the ECU is seeing when it turns on your fans.
BTW, when you say overflow tank, do you mean an expansion tank (that has a pressurized cap?) or a recovery tank? (regular threaded cap)
My method will work wherever the pressurized cap is, whether its the radiator or expansion tank.
A recovery tank simply holds discharged coolant from the pressure relief when the coolant is expanding.....this tank will have a simple threaded cap (no pressure rating). If this is the tank you have.....you'll notice that the hose connecting to this tank will be connected to the filler neck of the pressurized cap (wherever that is....radiator or expansion tank). That hole is so close to the opening of the filler neck that the coolant will overflow the open filler neck wayy before it starts filling up the recovery tank.
Here is some info from canton racing:
http://blog.cantonracingproducts.com...on_vs_recovery
Assuming the recovery tank is at the correct level and sits above the pressurized cap, no air pockets will be trapped in there.
And just to knock out another obvious, check if your A/C is on (if you have it). The fans may come on sooner when the climate control is on.