Why the tigers den does not work.?

Facilities multiply the stats of workers that are relevant to what their doing every 10 floors you clear. Cept the tigers den which does all.

For most its 10%, for caravan and church its 5%. That means if they have 5 like at the start, you have to reach lv20 for you to see anything because 20% of 5 is 1 :p

Employees only get stats when you go into mastery dungeons

other dungeons won't do anything

The training occurs automatically to all your active facilities whenever the Den is active. When you exit any dungeon, each facility except for the Tiger Den, Caravan, Church, and Satellite Cannon increases a single stat by 1% for each floor cleared (rounded down), while the Den increases all stats that much. The other 3 increase 2 stats, but only .5% per floor.

A more mathy answer:

Stat Increase = Initial Stat x Floors Cleared / 100

Rounded down (use 200 instead of 100 for Caravan, Church, and Satellite Cannon). This means that you will gain no stat points unless you go down at least this many floors:

100 / Initial Stat (or 200 / Initial Stat for Caravan, Church, and Satellite Cannon)

Rounded up.