While I was working for the City of Houston, I was responsible for obtaining Engineering Test Results for asbestos containing materials in city buildings. I do not recall having seen positive results for ceiling tiles. Having a tile tested for asbestos materials would best answer your question.
There are federal regulations regarding handling and disposal of asbestos containing materials (if found). Your best action at this time would be to have a tile (or several) tested by a reputable firm. Don't depend just on a Contractor.
There are slight variations of the regulations when it comes to you as the Property Owner.
As a Realtor I cannot advise you, except to advise that you obtain creditable testing results.