Frontier haven't said a lot about exactly what control/exploit represents, but they did make clear when the major Federal military base of Beta Hydri became an ALD Control system early on in Powerplay that it was a very "soft" and indirect form of power, and not anything that would noticeably affect the Federation military presence there.
So, realistically and for lore reasons, the exploited system might NOT be as loyalist as a controlled system would be.
It may also depend a bit on how the exploited system itself is run. There's a lot of potential gradations based on the in-game effects that you can use to tune how happy the local system is with it.
So for example, Hudson gives +20% security to Federal exploited systems ... and -40% security to the others. Or Patreus gives +30% volume and +5% price to high value goods trade in Imperial exploited systems ... and -5% price in the others. So some might be happier with the arrangement than others.
You can also look at the Control ethos for the power relative to the governing minor faction - for example, Mahon has the Finance Control ethos, which is strong against Corporations, and weak against Communist, Cooperative, Feudal and Patronage. So an Alliance Corporation might be very happy to be exploited by Mahon, while an Imperial Patronage would absolutely hate it.