Keep it Simple:
Orbs can be separated into Affinities: Example Tier 3 stage 1 waterorb can be applied to only a tier 3 water illuvial.
Example: Tier 3/Stage 2 water orb = 2% stat boost to a slappins/slashins/stabbin attack speed.
Tier 1 Illuvials:
Burn a Tier 1 Stage 1 Illuvial → Get a Tier 1 Stage 1 Orb that boosts a stat by 1%.
Burn a Tier 1 Stage 2 Illuvial → Get a Tier 1 Stage Orb that boosts a stat by 2%.
Burn a Tier 1 Stage 3 Illuvial → Get a Tier 1 Stage 3 Orb that boosts a stat by 3%.
Tier 2 Illuvials:
Stage 1: Burn a Tier 2 Stage 1 Illuvial → Get a Tier 2 Stage 1 Orb that boosts a stat by 1%.
Stage 2: Burn a Tier 2 Stage 2 Illuvial → Get a Tier 2 Stage 2 Orb that boosts a stat by 2%.
Stage 3: Burn a Tier 2 Stage 3 Illuvial → Get a Tier 2 Stage 3 Orb that boosts a stat by 3%.
Tier 3 Illuvials:
Stage 1: Burn a Tier 3 Stage 1 Illuvial → Get a Tier 3 Stage 1 Orb that boosts a stat by 1%.
Stage 2: Burn a Tier 3 Stage 2 Illuvial → Get a Tier 3 Stage 2 Orb that boosts a stat by 2%.
Stage 3: Burn a Tier 3 Stage 3 Illuvial → Get a Tier 3 Stage 3 Orb that boosts a stat by 3%.
Tier 4 Illuvials:
Stage 1: Burn a Tier 4 Stage 1 Illuvial → Get a Tier 4 Stage 1 Orb that boosts a stat by 1%.
Stage 2: Burn a Tier 4 Stage 2 Illuvial → Get a Tier 4 Stage 2 Orb that boosts a stat by 2%.
Stage 3: Burn a Tier 4 Stage 3 Illuvial → Get a Tier 4 Stage 3 Orb that boosts a stat by 3%.
Tier 5 Illuvials:
Stage 1: Burn a Tier 5 Stage 1 Illuvial → Get a Tier 5 Stage 1 Orb that boosts a stat by 1%.
Stage 2: Burn a Tier 5 Stage 2 Illuvial → Get a Tier 5 Stage 2 Orb that boosts a stat by 2%.
Stage 3: Burn a Tier 5 Stage 3 Illuvial → Get a Tier 5 Stage 3 Orb that boosts a stat by 3%.
Summary
Each Tier/Stage determines the percentage boost a shard provides:
Stage 1 Orb boost a stat by 1%.
Stage 2 Orb boost a stat by 2%.
Stage 3 Orb boost a stat by 3%.