This is completely normal for this motor - people have been noticing it for a long time even with the original VVT-i variant. All of these engines single or dual VVT-i have a tendency towards the rough idle in park, some do it worse than others. Obviously there is some variability in the motors themselves, but fuel quality can and does affect the tendency for them to shake.
The motor as released was designed to use premium fuel. When it was first introduced into 2nd gen Tacomas, Consumers howled about the "need" for premium and the next year (2006) Toyota de-rated its power from 245 to 239 and said it was designed for 87 octane fuel. In reality, Toyota didn't do a thing to the motor - it was always ran just fine on regular 87 octane fuel, it just self adjusted to the lower octane fuel, retarded the ignition.
Most of these engines happily run on 87 octane fuel, but not all of them. I have an '07 Tacoma, a '12 Tacoma and '13 4Runner. The '07 Tacoma and the '13 4Runner run fine on 87 octane. There is a slight roughness at idle in park, but no big deal. The '12 Tacoma has always been rougher in park. In addition, I've noticed I get a little detonation when accelerating in lower rpm ranges sometimes. I have also found that swapping to 91+ octane makes the idle about the same as my other engines and eliminates the pinging.
When running premium the '12 Tacoma gets about 1mpg better mileage than without which means the premium fuel is a wash as far as cost. I run premium in the '12... The motor was designed to be able to run on 91+ octane and get benefits from it. It is not surprising that some individual engines are more sensitive to fuel quality. Run it on premium if you notice a difference, it will probably get slightly better gas mileage which will effectively pay for the difference in fuel quality.
Regardless, don't stress about the motor being rough idling in park - they all do it to some degree, it is normal and nothing is wrong.
David
