Apple sold two different versions of their 27” displays - the former being the LED Cinema Display (which uses DisplayPort connection standard), and the latter being the Thunderbolt Display (using the Thunderbolt connection standard). Are you sure you have the Thunderbolt model?
The reason I ask is that the Thunderbolt 3 to Thunderbolt 2 adapter does not support DisplayPort displays. Per this support article, if you have the LED Cinema Display then you will instead need to purchase a USB-C to Mini DisplayPort adapter from a third party, like Startech for example.
If, however, you do indeed have the Thunderbolt Display, then it should be working with the adapter you currently have and may need to do some further troubleshooting to understand why the Mac mini is not picking up the Thunderbolt connection.