Extremely Weird Problem

So I recently purchased a 2010 prius with around 145k miles on it. It runs really smooth 99.99% of the time but I've come across a weird problem. I have no coolant consumption and I recently changed spark plugs. The problem goes like this, when the engine is off and I start accelerating, its smooth until the engine kicks on then it starts shaking like there's a misfire, so then I let off the gas completely and accelerate again and it completely goes away. But here's the weird part. It ONLY happens when I go on an EXACT turn at a green light. If the light is red then the engine has the opportunity to turn on before turning left so It doesnt happen. It only happens when I come up to the light green and slow down to make the turn then accelerate. The only other time I've had this happen was the known problem where you dont let the car go through a warm up cycle before turning it off the night before, so it misfires at start up. Again I have no coolant consumption and the oil wasn't milky at the last change. Can someone please help?? Thanks!

 

So its only at this certain light in my city, it has never happened anywhere but at that turn. Its just a green light where you yield to people before you turn left on to a 55mph street. If there are no cars to yield to, then when I slow down to make the turn, the engine is not on so when I start accelerating when im on the road I turned onto, the engine will kick on and misfire or something along those lines. It happens every time only at that light, no where else

 

Oil level is good, im changing it in a few hundred miles

 

I bought it a few months ago used, I can get it scanned at autozone probably

I honestly don't think that is the problem because right when I let off the gas and immediately go again its perfectly smooth, I think it would take some more time before the oil exits the cylinder

 

No, it only shakes on a green light and there are no cars i have to yield to. If there are cars or its a red light then the acceleration is fast enough to fire up the engine before turning so it doesnt shake