While there's no set rule about The Hunt that forces you to shout/announce when you find a hunt monster with your group, there's also no point in introducing some kind of "competitive" aspect to the hunt by keeping it for yourself.

"I'm killing this monster with my group without telling anyone else, so other people don't get anything" doesn't make any sense and does not provide any kind of advantage or bonuses whatsoever.

In fact, it promotes bad behavior and calls up a vicious circle where everybody will try to "ninja this hunt monster because others are doing the same!".
Which means that less Allied Seals are created overall and thus, slowing down the global progression of the server.
It also obviously creates disparities between people able to keep up and ninja some monsters, and players who can't. This will then lead in SE having to take both side in consideration when creating new stuff, or, completly ignore the overstuff ninjas because they're just a minority.

So, in general, preventing others to grab some Allied Seals from a Hunt Monster you find is giving overall bad results.
But, again, nothing prevents you to do that. If you enjoy trolling and/or being selfish, even if it hurts you in the long run... well, feel free to do so. On the other side of the coin, you have to be prepared to be hated by a lot of people... but, that's your own choice.