We just ripped up the carpet and cork tiles in our 1955 built Eichler. The contractor is having a sample tested to see if it asbestos underneath. We won't know for a few days. Anybody with a simular era home have any experience with this?
I can't answer your question, but would really appreciate knowing the answer to your findings. (And what, if anything, you plan to do about cleaning your house after the demo.) We just ripped up carpet, and the cork and vinyl underneath and are testing the vinyl but not the cork. Our home is 1953.
You will most likely find asbestos under your Cork Tile.
My 1955 in RSM had it and most other posts here on the site state same.
This is only a problem when you scape off and create dust. There are great posts here about techniques to avoid this.