You're playing a character that willingly consorts with devils. The imp is a devil, therefore it is an outsider with all the appropriate subtypes it comes with. Nothing in the class changes that fact. It says it acts as a druid's animal companion simply for the fact that--unlike a wizard's familiar--the imp's abilities will increase significantly as the diabolist increases in level, therefore it advances as an animal companion. That doesn't mean it is an animal companion.
The Share Spells section is saying that the ability works like the wizard version, not the druid version. That's all it's saying. Though I'm not certain why they make the distinction, because the ability is virtually the same for both classes. Probably because the druid version has the restriction "Spells cast in this way must come from a class that grants an animal companion." So it means that you can cast spells with a target of "You" on your imp companion instead of yourself.
But nothing in the rules for the imp companion in the prestige class say what type it is. Just like a Ape animal Companion is a complete different creature with different stats from an Ape in the Beastiary, the Imp companion only gets what is listed in it's animal companion states and the prestige class write up. Assuming strict rules as written.
Don't get me wrong, I want it to count as an Outsider[Lawful, Evil, Devil]. But I'm not sure that it does strictly RAW, and no amount of logic or story fluff will overcome that for PFS.
Unless the rules specifically say there is a change in type, like the wizard's familiar rules stating they are considered magical beasts rather than animals, then it remains the same.