Its called Variable Valve Timing because its always running. From the second the engine starts, VVT is attempting to adjust to conditions. When it can't, gets stuck, it will tick for 1-2 seconds. Unlike Honda's VTEC that uses two sets of cam shaft profiles – one for low and mid range rpm and another for high rpm operation, VVT camshaft timing is varied using oil pressure according to engine revolutions, throttle position, engine coolant temperature and intake air volume.
VVT operation depends on hydraulic oil pressure that arrives through a long winding path of tiny oil passages. So tiny they are known as "vanes". Its critical the system stays clean. Its critical the system maintains proper oil flow and pressure as fast as possible to prevent that annoying startup tick.
Proper lubrication comes from a combination of oil pressure, flow, and film strength between moving parts. Oil pressure by itself is no indication of proper engine lubrication. Oil pressure is managed by the oil pump and relief valve. Thick oil will have higher pressure because there is more resistance to flow. Too high and it will flow out the oil pump relief valve back to the sump, lubricating nothing including the VVT system.
As stated above, thick oil will have higher pressure because there is more resistance to flow. Add that to the tiny "vanes" of the VVT system and you have a oil flow lag as compared to the rest of the engine. By as much as 1-2 seconds. No coincidence that's the duration of the noise.
Modern thin oils have better flow, better viscosity modifiers to manage film strength. That means better lubrication and cooling, keeping pressure within spec. Tthin as possible is a good thing, especially for the VVT-i system.. "Thin as possible" meaning some older engines have mechanical issues like wear/higher tolerances, valve seals, rings, etc. causing oil consumption that may prevent its use.
