Sentinel passive "Time and Faith" (25 health and 10 mana regained when you directly use Rive, Vengeance, Smite or Multistrike) does not work as described and very oddly:
Using Smite regains no mana UNLESS you were very very low or negative mana at time of cast. If you are under ~10 mana it also wobbles around costing mana then regaining it (even if your spell cost is 0). When you are over ~10 mana you get no mana back
I did not test for Health (hardcore / no way to lower health on dummy)
It works for me. It sounds like you took one of the increase mana nodes (in particular Fissure).
By default smite costs 3 mana, so you should gain a net of 7 mana when you cast it (if you spend all your mana and then start casting smite you’ll see it jumping up slightly each cast). If you have Fissure allocated you should lose 3 mana when you cast it (which if you’re recovering 3 mana/sec will look like mana isn’t moving).
Also, the life gain works as well. You can equip Exsanguinous or Lasts Steps of Living to test with dummy.