Your poison is Aluminum Phosphide.
Your pet is (Surprise!) a camel.
Let's get into it.
Aluminum Phosphide is a highly toxic powder. When it reacts with water or stomach acid, it produces Phosphine gas, which is highly toxic to cells. Phosphine gas is especially deadly when inhaled. Poisoning normally starts to show symptoms within a few minutes, in humans. Phosphine gas is also pyrophoric, exploding spontaneously around 38°C (100°F). Aluminum Phosphide consumption, and subsequent Phosphine production, was suspected in the tragic death (Warning - graphic news article) of a patient in India who exploded on the operating table while being treated for poison. Note, this is an extremely rare case, perhaps because humans' resting temperature is a bit below 38°C (although the stomach temperature is close). Give your victim a mild fever and worse luck, if you must.
But why a camel, of all creatures? First, their gut acidity is much milder than that of humans, around a PH of 6.4 vs 1.5. Thus, Aluminum Phosphide will turn to Phosphine gas somewhat more slowly than it would in humans (how much, I don't know). Second, their resting temperature, in the right conditions, can be notably lower than that of humans, dipping to 34°C. This effectively prevents the automatic explosion of Phosphine in a suitable camel. Third, they seem to be obligate nasal breathers, or at least breathe nasally as a primary means is respiration (I couldn't find a great source for that yet; suggestions welcome). This would prevent the camel from being as affected by the respiratory effects of the Phosphine gas, although the direct cellular damage would still take place in the gut. Finally, and importantly, camels are big, tough animals. Toxic effects are likely to be slower for them than for humans, for most poisons.
So when the villain laces some dry food with Aluminum Phosphide, being sure to keep it out of moisture, the camel will last for a few minutes, but the human, if particularly unlucky and feverish, has a chance of a very unusual and unpleasant demise.