Don’t sweat it. People tend to panic at the word asbestos
with little reason.
Those tiles encapsulated any asbestos but the tiny amount
exposed at the breaks and little if any of that was turned to fine dust.
Fine dust is the only kind of asbestos that can hurt you.
If you’d cut them with a saw or something, you’d have some small worry,
but even then, most people who have gotten sick fro the substance
suffered long, heavy, and repeated exposures. You didn’t.

Asbestos related diseases are very dangerous. Asbestosis is one that develops over a long time period in the lungs of people who were exposed to airborne particles that they breath in. This is most common in chain smokers who were exposed for several years on a regular basis. The tiles you speak of may contain asbestos, unless it was friable, the danger is very slight. Since these were tiles, even broken ones, there was very little in the air because the fibers were encased in a bonding material.
I have been exposed over 60 years, and been tested for 30 years, no signs at all. I quit smoking 40+ years ago.

I could be mistaken but I believe only the 10 by 10 tiles are the ones that had asbestos in them.I wouldn’t worry either way though because I doubt a week of exposure would have any effect.The particles are heavy and would fall to the ground if they contained any.I doubt that you breathed any.Don’t worry.You’ll won’t be affected.Good luck.

I have been exposed to it many times doing construction work for over 50 years and have been examined three times and have negative results and am now 77 and no sign of any cancer or lung problems.
Hope you have same luck. I also knew quiet a few pipe insulators who were in constant touch with it for years and are OK.
Also knew some electricians who were not so lucky
Only tests can prove or disprove any lung disorders.