Tile parquet is coming off the concrete surface
First the flooring is fine as long as it isn't warped.

To me there seems to be three main install issues:


You do not have enough gapping around the perimeter of your install.
If you are going to glue these down on concrete they would almost assuredly need some space between them - might use 1/32 spacers.  
The glue dries to brittle.  Doubt this glue was meant to be used for wood to concrete - you are lucky you used the wrong glue as it let the squares pop up clean, relatively.


So your floor buckled.  This is due to:


is this flooring meant to be installed on concrete?  What does the manufacturer's info say?
has your house had wide swings in humidity?  This will cause the wood to expand, especially next to cool concrete.
have you had a lot of rain?  The concrete will keep moisture without revealing water but this water will escape up.
did you let the flooring sit out for 3-4 weeks before installing?


What it comes down to is that this flooring is probably not a good solution for your situation.  It could have been a humidity swing but you shouldn't be required to keep your house like a climate controlled wine room to keep your flooring from buckling that much.  This is a solid 9 out of 10 on the buckling range.   Expect that if you glue the squares down again, even with a little gapping added, you will probably get buckling in the future.  At the very least you are probably going to need to introduce a vapor barrier and subfloor to install a glue down.  I don't think I have ever seen glue down wood to concrete other than large apartment buildings.

My guess is that you and the previous owners are very lucky the install lasted that long and probably have been keeping house at normal ranges.  In my area we see this all the time, and it is buckled just like yours but not usually as bad.