@Rainbow706 , You are wrong. Your own evidence shows that the Generic Quest - 4 Relics behaved correctly in your second example.
Your description of the second questline:
"Everything from then till Province 7 was right.
Again screen shot 3 shows 1KP, 4 Elixir, 1 ensorcelled endowment. It only registered on the Generic Quest as getting 3 relics."
Screen Shot 3 does show 1 KP. 4 Elixir and 1 ensorcelled endowment.
After you completed the 3rd round for Province 7, as there are now 3 stars showing for that province. This is the reward you
will get when you complete the
4th Round for Province 7, which will be unlocked in another 16 hours. Screen Shot 1 shows the rewards that you
were going to get when you finish the
3rd Round of Province 7, 1 KP, 3 Elixir and a Broken Shard; the province listing at that point showed only 2 stars, as you had completed 2 Rounds for that province.
This is the reward that you
just got.
3 Elixir Relics. This is the quantity that was registered for the Generic Quest - 4 Relics.
3 Relics.
As for the first example, according to the Tournament Calculator, the rewards for the 3rd round of the first two Provinces are 1 Relic+1Broken Shard and 2 Relics+1 Power of Provision, for a total of 3 Relics. Not 4, 3.
Let me mention another observation. Notice how, in both pictures 1 & 3, some of the listed rewards show 48 Ranking Points and some show 42 Ranking Points? 42 Ranking Points is part of the reward for finishing a Province for the 3rd Round, while 48 Ranking Points is part of the reward for finishing a Province for the 4th Round. Look at the stars, look at the ranking points.
The Generic Quests - 4 Relics have not been miscounting 4 Relics as 3. In both your examples, completing Provinces 1&2 in Round 3 and completing Province 7 in Round 3, you only earned 3 Relics, not 4, and the Generic Quest correctly credited you with having received 3 Relics both times.
Not a true bug.