It’s hard to avoid having target staff think that. They are scared of what is going to happen to their jobs.
Relationship building is important. I think repetition is also important – continually talking to people about what you are doing there and how you plan on helping.
Time will really give people a chance to get over the shock of the acquisition. You also need Management and HR to give some direction (when they can) as to what the organization will look like after the integration. Once people have a sense of what is expected to happen, they will settle back into their routines.