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I have heard about the reward system related to Boss killing. How does it work? How can I get my reward?
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I think this question is related or very similar to this one https://www.tibiaqa.com/294/where-is-the-reward-chest
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I've put it before in question thread which You linked. Ellotris gave me the advice to move my answer to the new question "How can I get loot from a boss" due to the fact it wasn't strictly an answer to His question.
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Correct. This question is related but different than "Where is the reward chest?"

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There is a Reward system for Boss fights implemented with Update 10.2 Bosses drop a reward container  ---> where You can find Your prize. If You don't loot it, it is still possible to check Reward chest which is located in adventurer's guild (but only 7 days after killing the boss).

Until now, the following bosses are affected by the new system:

+2 votes
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- Rareness

The labels of creature loot rareness are 'always', 'common', 'uncommon', 'semi-rare', 'rare' and 'very rare'. No distinction between regular and boss creatures is made.

Rareness       Drop Chance      Example (from Demons' loot)

Always            100%                  Some items from quest or event creatures

Common         ≥ 25%                 Platinum Coin

Uncommon      ≥ 5%                  Demonic Essence

Semi-rare         ≥ 1%                  Fire Axe

Rare                  ≥ 0.5%              Demon Shield

Very Rare         < 0.5%              Demonrage Sword

The names and percentages of these labels are in accordance to Bestiary's rareness classification. The system to bosses is the same.

- Level of participation

It is not known with certainty the formula that determines the level of participation of a player in a fight, but it was clear that causing more damage in a boss is not a primary factor that guarantees the best items. In addition to this factor, they are considered:

If the creature is being blocked from escaping.

If the players are giving support in the fight against the boss. In the case of members who are participating, catching the boss with magic wall, attacking the boss.

After the creature is dead, the elements of the creature are divided to the players depending on the level of participation and the rarity of the items in the loot. Maybe the following table helps to understand.

Constitution of the Loot                                                                   Poitns           Level

Item Common                                                                                     10~40pts           1

Item Common + Item Semi Rare                                                        40~60pts           2

Item Common + Item Semi Rare + Item Rare                                    60~80pts            3

Item Common + Item Semi Rare + Item Rare + Item Very Rare        80~95pts            4

Item Common + Item Semi Rare + Item Rare + Item Always Drop    96~100pts          5

Another way to explain this can be (THIS IS WORK OF DAIDUM):

Lets say damage is 50%

Healing 30%

Damage you block from Boss 20%

So the probability will Split between every hitter And healer. Then you Will multiply that % per the % of loot statistic of the rare or boss loot.

So the algorithm Will be something like this:

X = % of loot, D=damage u deal , H = healing people , DB= damage blocked from Boss, L=% item drop

X= (D+DB+H)* L

...