To be fair, Monet did have an awkward "Joker will kill me if something happens to Caesar" moment when she was introduced, suggesting that she might not work for Doflamingo willingly.
I wonder if Oda made her say that just to toy with a certain part of his fanbase, especially since that line was totally inconsistent with later reveals (her motivation being absolute loyalty to Doflamingo + Doffy being extremely forgiving towards failing subordinates).
Anyway, Oda might be teasing here and there, but he's never playing games for long. One chapter later we saw Monet gleefully drugging children, at which point the discussion should have been over.
To be fair, lots of minions can be scared at the thought of pissing off their bosses if they messed up despite having legitimate loyalty and sympathy for their cause. Just look at Jack's subordinates. Hell, I think even somebody as intimidating and reckless as Jack might be a bit on edge if he knew that, for example, he did something to mess up Kaido's precious SMILE operation. Spandam was also intimidated by CP9 even though they worked FOR him due to them being bloodthirsty super humans, and he's easily intimidated by Lucci now as his subordinate in CP0.