Here's how I imagine time travel.
Suppose this time traveler is in 2012 and a time machine has been invented around 1930 or maybe even before, but 1930 has a set savepoint, which tells the machine exactly how Earth looked at that time. (minus position in solar system, unless the machine has that much energy, but the amount of energy needed for that would probably require more than material the size of a whole planetary system being converted to energy, moving Earth would probably only require a planet a bit bigger than Earth to be destroyed to give its energy for this).
A 1) the time traveler is that red dot and there is a red line connecting him to the past (and that past is nowhere actually, as it is converted into the traveler's present, all matter is there in the present, under some form or another).
That red line represents everything that had contributed to the body of the time traveler and even the machine's material (knowing that the machine is immune to the effects of reversal, and the traveler being inside it would keep the traveler's material safe too).
The traveler is in 2012.
The green dot is the traveler's grandfather. He holds part of the genetic material that will compose the traveler's parents and the traveler ultimately. He was born in 1930. 1930 is not somewhere else, 1930 has been converted to what is 2012 in matter form. It does not exist somewhere in this universe simply as "the past". The past no longer exists in that form.
A 2) The traveler makes the time machine reverse Earth back to its state in 1930.
In reality, it is really 2012. But the Earth will look like it was in 1930. Everyone will think it is 1930 and will act like it is, because their memories are of that time. Even dead people would be alive (note that this example does not follow the idea of life = soul though so at this point a lot of people would probably say "Impossible." so stop reading if you dislike this point of view) because the records state that they were alive in 1930.
The traveler meets his grandfather and kills him. He then waits 82 years, exactly the difference between 1930 and 2012.
A 3) When he ends up at 2012 (assuming he has lived that long), not only that he doesn't have a grandfather or parents or he finds out that he was never born (even though he has an ID card) but he realizes
he is actually in 2094 in reality (this because he has only changed matter, time would be irrelevant since he only wanted to see a certain outcome of events in a "what if" scenario).
Now let's take case B:
B 1) Time traveler in his current time in 2012. Had a grandfather born in 1930 but again the past is not "somewhere out there", it is converted into 2012 state. So there is no separate dimension where it's 1930 at this time. It does not exist like that, but the machine has recorded what 1930 looked like and the changes along the way till 2012.
B 2)Traveler does NOT kill his grandpa but only reverts the planet back to its 1930 state just to meet his grandpa.
The moment he does this, he also knows that his genetic material and every other creature that had contributed to building his body by serving as food for him / his parents are all inside his body so they will not be encountered or will not be encountered whole in the new version of 1930.
Again, in reality it would still be 2012, with a 1930 setting (people that died are alive again, wars that happened didn't happen yet etc).
There will not be a duplicate of the time traveler, so even though his grandpa lives and has a child which will be the traveler's father, the traveler's parents either will not have a child or will have a child, but that child will NOT be the traveler. It will become the traveler's brother (that he never had in the original timeline).
After the 82 years pass, when it should be 2012, the traveler (if still alive) will have a brother that will probably be as old as he was before leaving with the time machine towards the past.
The time in reality would be 2094 once again.
In all these examples, the moment the time traveler begins his travel, the 2012 existence of Earth is destroyed and converted to its existence after the model of 1930, with the difference that it lacks the material that the traveler's body and the machine have retained. So it would not matter who he kills in this new 1930, it will not affect him but will create a new 2012 (which in reality, since it is only SPACE that is modified here, is 2094). On the other hand, it matters who avoids getting affected by the machine. So anything that is excepted from the reversal will affect the outcome of the reassembly of a 1930 setting.