It made no sense for these aliens to find a specific era in hostory where they could "hide" thier work behind an epidemic of some sort.
The alien might not have had full control over their destination. The devise could send them to Earth, San Fransisco, in that certain year, and no where else at the moment. They took advantage of whatever travel connections they could make.
The epidemic could have been a fortuitous coincident for the aliens. During that time period, you would be hard pressed to find a large city without a on going serious medical problem.