I'm not sure if police state is the best term for it.
They allowed their lower castes very little. Communication time constrained, quality of life restricted, food restricted (at times at least).
If the Clan gives you everything you are allowed to have, and they limit what you do have, is that a police state? Or just a restrictive one?
And btw they weren't afraid to use public, open face violence and brutality to crush any misbehavior.
That's not quite the same thing as traditional police state in my mind. It's more like a military occupation. Just one of your own people. And since the Jags were quite open about it, they could use obvious public warriors to do some of this. But they could even enforce this through their lower castes. If the technicians control the chatterweb, then the jags are telling the technicians who manage the chatterweb how much time to allocate. If the Jags are limiting consumer items, then they'd be telling the Clan's lower castes how much of such things to make and distribute.
It wouldn't just be a function of a Watch, or the warrior caste, it would be a bunch of Clan-wide policies, enforced in part by the lower castes themselves.
All that being said, you could be right, they could have had a large Watch. Or maybe a larger than average police force as a percentage of their population. I'm not sure anything tells us from canon sources. So, it's an area of pure speculation, unless there's a source I'm unaware of that addresses this.