There's a big difference between tempo and rep counting. Counting reps is simply a means of measuring set volume, whereas tempo is rep TUT.
I feel that lifting tempo doesn't change much at all (unless momentum/bouncing is used). Lift as forcefully as possible without using momentum; you'll not be able to lift this load much slower without lowering the amount of load or reps.
So to me, this answers the question of whether to time your tempo - it's pointless; you'll not be able to get more TUT unless you get stronger. If you deliberately slow down the reps, you won't manage as many reps (but the TUT will probably be the same unless you got stronger/weaker).
Slowing down the tempo (not timing the set/counting reps) doesn't target different muscle fibres IMO...it just makes it harder to track progress.
TUT is what counts the most when targeting different muscle fibres. And the easiest way of tracking this is reps/set (asuming you aren't deliberately focussing on slowing down the reps)...it's all pretty natural (you'll slow down towards the end of a set).