In Lucy's fight with Angel the Gemini transform into Lucy and it makes her spirits do whatever she says, but when Angels spirits learn about Lucy's love for spirits they start disobeying Angel how does that work? Shouldn't they be under the same I can't disobey my master rule?
The spirits are their own people. Loki (Loke) says this when he has a flashback to his previous owner. They share feelings with one another (Demonstrated when Loki and Aries are both hit; they tried to grab each others hands).
They are under the same "can't disobey my master" rules, however they can stand up for what's right (Loki did this with his former master, Karen Lilica). They can inhibit the wizard's ability to summon another spirit since they know that summoning 2 spirits at once is taxing on the user's magical abilities. This would be considered rebellion, the contract (still vague on the community) is a bond that states that a spirit is under the wizard's control until their key is broken. It never once was stated in the manga and anime series that the spirit can't rebel.