If the tiles were manufactured in the United States, after 1989, they should be asbestos free. After hurricane Katrina, there was a shortage of building materials. So some companies shipped in Chinese supplies, some of which were made with asbestos. I'm a restoration professional. So I run into it from time to time, but it's not incredibly common.
We have a drop down/suspended ceiling in our bedroom that had some water damage to it. We took it down and now I'm thinking "oh great" it might have asbestos. The ceiling was put in around 2005 and i can't find any info on the ceiling tiles. They are like an acoustic/insulation type.