I've unlocked tempered monsters and I occasionally follow tracks for them, but they never seem to end up with tempered monsters while on expeditions. Do you only find tempered monsters on investigations/quests or can they also be found during expeditions?
Following tracks of tempered monsters doesn't lead you to them, it unlocks tempered investigations (though I don't think this is guaranteed).
I believe that aside from assigned/optional quests that have tempered target monsters, these investigations are the only way to find/hunt tempered monsters; they will not just show up on an expedition or other quest.
You can find them during expeditions also if you have enough patience and luck (no time limit) but it is easier on a tempered investigation.
So my recommandation would be expeditions until you unlock your first tempered investigation then just try to get the tracks of the monster you're hunting to unlock even more
More info on how to find them and unlock the quests you can find in the below thread: