No, that's just kind of how CB sounds. It's a tongued/accented start to the notes. The legato transitions all have a slight tongued transition as well.
In earnest - I know a lot of people have used cinebrass forever and love the sound. But at this point I'd say Cinebrass is simply outclassed by better sampling and scripting that has come along.
Yes, you can get workable results with Cinebrass. Yes, it has a nice overall tone. But it really is not all that consistent (certain articulations have different volumes/dynamic ranges/etc), the instruments have fairly limited dynamic range (core doesn't really go brassy loud), and there's concessions all over between core and pro. There's also a lot of warbly notes, a few tuning issues, and pro has some serious noise floor problems. There's also a lot of inconsistency in volume from note to note on the pro instruments.
Given how much more dedicated (and affordable) dedicated brass libraries have come out recently, and how many are set to come out over the next year, I'd say Cinebrass sits pretty far behind in terms of the competition. At this point other than a couple standout instruments I feel like Cinebrass was a mistake purchase on my end. It just won't see much use because I have more flexible, easier tools at my disposal.
It would be wicked if they had an update that took care of these things. But I think at this point Cinesamples would have to make an entirely new library with better sampling to really compete with what is available.