If you breath in once and breath out once in the past, you will mix past and future airborne germs and viruses.
You will leave some bacteria and viruses from the future in the past, and you will bring some past bacteria and viruses to the future when you return to the future.
And the bacteria and viruses transported through time are likely to have different genes and introduce those different genes into the populations of bacteria and viruses in their destination eras. Thus they will h change the gene pools of bacteria and viruses in their destination eras, and that will change the future evolution of new strains and species of bacteria and viruses.
These new species of bacteria and viruses will mostly be harmless but will include some harmful ones and some deadly to humans.
Thus some humans will die that would have lived, and some humans will live who would have died. Some of the humans who would have lived would have died without offspring anyway, and others would have had offspring who would have died out within a few generations, but others would have had descendants that would continue for as long as the human race survives.
Some of the humans who would have died will live longer but die without offspring anyway, and others will have have offspring who will die out within a few generations, but others will have descendants that will continue for as long as the human race survives.
If a human has a line of descendants that never dies out as long as the human species exists, his descendants will multiply and eventually include every single human being alive at some specific future date, and then all the rest of the humans who will ever be alive in the centuries and millennia and tens of millennia and hundreds of millennia of the future existence of the human species.
And the time it takes for a human's descendants to spread and multiply until every single human is descended from them should be only a few thousand years, perhaps 5,000 or 10,000 years.
So if a human from AD 2019 goes back in time to, for example, 10,000 BC or 20,000 BC or 100,000 BC, and breathes even once back then, they will cause all humans alive in AD 2019 (including their self) to vanish and never have been born, replaced by a totally different set of people alive in AD 2019.
So if a human from AD 1,000,000 goes back in time to, for example, AD 950,000 or AD 900,000 or AD 500,0000 and breathes even once back then, they will cause all humans alive in AD 1,000,000 (including their self) to vanish and never have been born, replaced by a totally different set of people alive in AD 1,000,000.
And if a time traveler brings bacteria and viruses from the past back into the future time of AD 2019 or AD 1,000,000, or whenever, that will eventually cause all of the people who are alive a few thousand yeas in their future to vanish and never have been born and be replaced by a totally different set of people for the rest of human history.
I have an idea for a story where the protagonist is sent to different times and places, including some on Earth and other planets at various times, and I have been wondering about how to avoid making that character the "Typhoid Mary" of the universe.
One idea is to somehow make that character's body and immediate area a "death zone" for bacteria and viruses, so none of them survive coming close to that character, and so he cannot transport living bacteria or viruses to the past or present of their world.
But if the character kills all bacteria and viruses they come near, every time they are sent to a new location in space and time, that should kill a lot of viruses and bacteria that would have otherwise lived, thus changing the future evolution of viruses and bacteria, thus causing some people to live and others to die and thus changing the entire future histories of those worlds.
One way to avoid that is to postulate that the beings who send the protagonist to various locations in space and time know from their time travelling that those are the locations in space and time they are destined to send the protagonist to, and thus the protagonist only kills the bacteria and viruses the protagonist was always destined to kill.
So you can see that I am interested in the best answers you get to your question about what is necessary for the time traveler to avoid changing the fate of worlds. Perhaps some of them will help me with my story idea.