Slate Vent Installed Incorrectly?

[Steebo69]

Hi, I'd appreciate any advice on this. Had some slate vents installed a few weeks back. We had some more work done the other day and somebody broke a slate next to one of the vents. This isn't the problem but what I saw beneath the broken slate could be as the sarking is visible. It's an old roof with no felt or membrane. Am I right in thinking both slates beneath the vent should have been cut to fit exactly around the vent box and up and under the slate above? So I shouldn't be seeing the sarking at all. Am worried the other slate beneath the vent might be the same, and the other vents as well. If so will this let water in? I've attached a pic.

Cheers for any advice.