When you gain Intelligence or +mana in Dota, it sets your new mana total such that it's the same percentage as before acquiring the item. If you have 50/100 mana, and your mana pool increases to 200, the game sets you to 100/200 mana to maintain the same percentage.

In this specific case, let's assume a mana pool of 500 with Arcane Boots equipped (+250 mana), and you have 200 mana remaining (200/500, or 40%). You drop the Arcane Boots, reducing your mana pool to 250, and your current mana to 100/250 (40%). You then use your Soul Ring, giving you 150 mana, putting you at 250/250 (100%) and pick up your Arcane Boots. The game looks at your mana percentage, and adjusts you to 500/500. After eight seconds the Soul Ring boost goes away and you drop to 350/500, essentially netting a "free" 150 mana (based on the 200/500 you started with).

As for whether this is a bug: like most confusing things in Dota, it's kinda just how the game works on a fundamental level.

When you gain intelligence or +mana in DotA, it sets your new mana total such that it's the same percentage as before acquiring the item. If you have 50/100 mana, and your mana pool increases to 200, the game sets you to 100/200 mana to maintain the same percentage.

In this specific case, let's assume a mana pool of 500 with Arcane Boots equipped (+250 mana), and you have 200 mana remaining (200/500, or 40%). You drop the Arcane Boots, reducing your mana pool to 250, and your current mana to 100/250 (40%). You then use your Soul Ring, giving you 150 mana, putting you at 250/250 (100%) and pick up your Arcane Boots. The game looks at your mana percentage, and adjusts you to 500/500. After eight seconds the Soul Ring boost goes away and you drop to 350/500, essentially netting a "free" 150 mana (based on the 200/500 you started with).

As for whether this is a bug: like most confusing things in DotA, it's kinda just how the game works on a fundamental level.