If time travel is based on a field of effect (rather than a portal-type event horizon), then each atom in the traveler's body materializes rather abruptly on the other end.
While the scientists have accounted for variations of ground height and surface composition between origin and destination (travelers begin the transition on an appropriately tall platform, which does not make the transition with them, resulting in a small fall upon arrival), they cannot account for variations in matter above ground.
Expected levels of atmosphere at the destination are filtered out by the process, but extreme variations in water content (fog, rain, snow, etc.) cannot be fully filtered. For the most part, the body tolerates this fairly well. Some parts of the body don't tolerate this well, though. Suddenly having your stomach filled with rain or snow can induce some significant nausea, or even vomiting. Lungs suddenly filled with moisture will, at the very least, lead to violent coughing fits. If enough water gets in the lungs (e.g. a heavy rain/snow fall)... as little as six tablespoons for a child... something known as secondary or dry drowning can occur.
“They may emerge from the water coughing, vomiting or seeming to have no obvious or distressing symptoms right away. Some hours or days (sometimes up to 48-72 hours) later, the patient may exhibit one or more of the following signs and symptoms:
• Changes in behaviour
• Shortness of breath
• Pale skin
“It is dependent on the type of water (salt, fresh, chlorinated) and
amount of water inhaled as to how severe this condition can be,” Heidi
“The damage that water can do to the sensitive airways in the lungs
can be significant and life-threatening. In all cases, it should be
treated as a medical emergency if any of the above signs and symptoms
are observed. After every submersion where the patient is having any
kind of difficulty breathing, they should always be observed in
hospital,” she says.
Moisture suddenly being added to the body isn't the only risk.
Our air is rarely empty. Insects, pollen, vegetation debris (seeds, leaves, etc.), or even pollution (assuming humans are present in the target time period) can occupy a human-sized space of air.
These contaminants suddenly appearing within our muscle mass would certainly hurt for quite a while, until cysts can form around the invading material. But if a dragonfly is suddenly embedded in your kidney, or a leaf suddenly bisects your intestines, you're going to have some pretty significant problems, possibly including bleeding from an orifice.