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Heya Grandma,
You receive chests from increasing Player Level. Your Player Level is a sum of all of your Hero Levels. The chest granted by your Player Levels is upgraded (not granted additionally to) to a Rare one every 5 Player Levels and an epic one every 25 Player Levels.
The only way to earn two chests from one level up, is every 10 Hero Levels (levels with a specific Hero) grant a Hero Specific chest in addition to the chest granted by increasing the Player Level.
In the example you listed above, you should have gotten a Rare Chest for hitting Player Level 110, and nothing from Imperius to level 2. You can check the Progression tab on your Profile to see how close you are to certain chests for Player Levels, and can check Heroes by clicking them under Roster to see how close you are to various Hero Level rewards.