If you get sick and bring your disease to the place you are going (for instance, because you were on a long and exhausting journey), you are going to be ill at your destination. You may have carried the germ for a long time, since you are used to it, and it will only strike if/when you are weakened.
If you get sick at your destination, it is not likely that you are allowed on board for the voyage back.
The only way a disease is going to make it back to your origin, is if it incubates longer than the time it takes you to board the ship and sail home, or if it incubates long enough to cause an infection spreading in the ship, but not wipe out the ships population.
Looking at the duration of the Atlantic voyage, this may pose serious constraints on the last scenario. More people are likely to get sick in the destination country. If only one party is traveling, this skews chances. Native Americans did not travel to Europe as far as I know.
Of course, travel over land is not isolated in the way a ship is and will have far fewer constraints.