I'm working with a project that is being captured 'wild' (i.e. without RS-422 control and no TimeCode signal) from a Shadow Telecine via an Aaton Keylink HD. It has TimeCode, Footage Counter and Frame Counter burnt-in.
I'm working in Apple ProRes 422(HQ) with an AJA ioHD. My project is setup as a 24PsF project.
When I set an in-point and an out-point in the clip (or in a Sequence) and then proceed to export it as a QuickTime Movie (same settings as project and timeline) the resulting QuickTime file has always an offset of two frames after the points I set. This happens when I export directly from the trimmed clip in the project window or from the Sequence timeline with and in-out range defined.
For example: I set an in-point where the burnt-in TimeCode shows 01:00:00:00 and an out point at 01:24:00:00, the exported QuickTime will start with a frame where the burnt-in TC shows 01:00:00:02 and will finish with a frame where the burnt-in TC shows 01:24:00:02.
One curious thing I've noticed is that, when I trim in a sequence, when the Canvas is showing me that I'm at point 01:00:00:00 the little thumbnail at the beginning of the clip in the timeline shows an image that is two frames later from what I see in the Canvas. If I 'pull' the in-point two frames earlier even though the canvas is showing me a different frame, in the thumbnail in the timeline I see the right frame and when I export then the resulting QuickTime begins at the right frame.
It sounds like a drop frame / non-drop frame issue you're seeing. I'd check that in your sequence setting window -- willing to bet that is what you're seeing. I haven't worked with 24psf much, but I know it reacts differently than 24p.