What you are getting from the teacher, and whether you feel it is valuable to you. Traditionally, the student-teacher arrangement was a relationship that could become akin to family. For some teachers, this can still be true. The modern business arrangement where a contract for money defined the relationship is fairly new in this context, or at least wasn't the way to get deeper, high quality training in the past. Honestly, it seems a shame to me that many people view this simply in terms of a business relationship: I pay you money, you teach me, and otherwise get out of my life. In my opinion, that cheapens and lessens the experience.
If someone has a big ego and is trying to control students and build an empire, I agree that is a school to avoid. However, in the above described relationship, telling the teacher that you want to train something else sends a message that you do not value what he is teaching you, and you do not value your relationship with him. And it is exponentially worse if you do it on the sly. It sends a message of disrespect. But context matters, all of this only matters where there is a stronger relationship than a mere financial contract.
From what I've seen, a teacher who isn't driven by ego would not try to control the students life. However, he might tell the student, sure go do what you want, study wherever you want, but then I will no longer teach you. It's because learning a comprehensive system requires focus and dedication. Training elsewhere means you don't want to give the focus and dedication needed, so why waste time teaching him, when his attention is elsewhere?
Some teachers won't take a student if they know the student still trains elsewhere, or will only teach the student the very rudimentary aspects until the student makes a formal departure from the previous teacher and declares a desire to be a serious student of the new teacher. With traditional Chines teachers, it takes time and dedication to prove you are dedicated and worth his efforts to teach you well.
A lot of people don't realize this, it is clearly the case with the OP, so I caution him to be honest with his sifu and see what the response is, or he may be burning bridges without realizing it.