The doctor guy injects Snake with the exploding capsules. He then says “tell him”. Hauk looks mad. Snake says “tell me what?” and chokes Hauk. Hauk then tells Snake about the exploding time limit.
But Hauk looked mad when the guy said “tell him”. Was he not planning on telling Snake about the capsules? Then there is no point, because the capsules have no motivating capacity if Snake does not know about them.
Maybe the doctor was thinking that Snake was going to be considered expendable: Snake saves the President (the Presidential Pardon was dangled out there as incentive), but not told about the capsules. The explosive charges are allowed to detonate, so that Snake can’t embarass the administration later, and/or the President doesn’t look weak on crime by Pardoning a high level criminal.