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Thank you for your feedback.
If I could change the time base in Encore, it would then affect my video and audio tracks which are correct though. Only the subtitle tracks causes me this issue. Also, Encore proposes only one 23.976 time base, so there is nothing I could change on this side.

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Dealing with great weirdness (see below), I tried to download a bunch of free apps (Subtitle Editor, Subtitle Workshop among others) and so far I could not find any cheap solution to my problem.
Neither Subtitle Editor, nor Subtitle Workshop would work. The app just won’t install (running Windows 7 Family on Bootcamp). Given I feel my problem comes from Aegisub, I thought I would install its latest version… then I remember why I sticked to an older version: their latest version won’t install (Mac OS10.8.5).

I need to export an alpha sub station file to import subtitles in Encore CS6. I do my export in Aegisub. So far so good! But that’s about it! My video is 23.976fps. In Aegisub, all my subtitles are perfectly in sync with both the video and the audio files (2 separate media). Upon export I find out in Encore that the subtitles drifts increasingly… by almost 3.5 seconds per hour. End result, my movie is almost 2 hours long and at the end of the movie the subtitles are about 6.5 seconds late (while it’s in perfect sync in Aegisub).

As said above, I spent hours on searching on the web. All those good free apps that I hoped could resolve my issue just won’t install. The only thing I found was Annotation Edit. With a simple click in the preference settings (switching the time base to 23.976) would fix it. All the time codes in the .ass file get corrected. Ok… but it’s a pricey solution as it sells for 300€ (I saw someone mentioned it costs 29$… I guess it’s a typo).

Would anyone have a clue how I can resolve my issue besides buying Annotation Edit?
I lurked at every single settings in Aegisub, but could not find anything. It’s weird we just can’t change the timebase in Aegisub (not talking of converting the frame rate upon export… obviously it doesn’t’ work as it translate time codes with a wrong time base info in the first place).

Thanks in advance for your feedback.