So, here is a simple guide to ensure you get the most out of the interaction between your raid composition and your Imp:
1. Summon your Imp before the raid starts casting their buffs.
2. Right-click on Phase Shift in the Pet Action Bar, or open your Spellbook, click on the "Demon" tab and right-click on Phase Shift. This disables auto-cast. Auto-cast is clearly visible as a little dots of light circling around the border of the spell. Fire Bolt, Fire Shield and Blood Pact should be on auto-cast.
3. Click on Phase Shift. This removes Phase Shift from your Imp.
4. Ask for appropriate buffs on your Imp if any are missing. Don't be shy about it! Blessing of Might and Horn of Winter are not appropriate buffs.
Woohoo!! At level-80, I don't worry about this pet. He doesn't aggro very much, so I don't need to hide him. He's free to resummon.