I use Logic... a lot... But this topic is a little over my head, so what I hope to do is help you troubleshoot your problem.
Logic is primarily a MIDI based applilcation, although it will handle video tracks and SMPTE locking (never used it this way... so... again... over my head.)
FCPX expects audio to be 24-bit, 48kHz sample rate. Logic *tends* to export 16-bit, 44.1kHz by default (if you're not paying attention). As far as I have been able to determine, FCPX will try to conform not only the sample rate (44.1 to 48) but also the bitrate (16 to 24). Both things can cause synchronization problems.
I have had my best luck synchronizing audio by Bouncing the track to AIFF 24-bit 48kHz out of Logic -- and not trying to export the audio any other way. Bounce is available from the Output slider in the Mixer. Select the PCM Destination (check and select the line) then, set the Type to AIFF, Resolution (24-bit bit rate) and Sample Rate (48000) [File Type Interleaved, Dithering None]. [Logic exports the audio at project settings, and then does a conversion to the "alternate" settings in a second step...]
If that doesn't work, the next thing to try is to select the audio clip (assuming it is separate from the video to begin with) and select Conform Speed from the Retime menu (the clockwise turned arrow with the spedometer dial icon.)
If worse comes to worse, synchronizing audio to video manually in FCPX is not really that big a deal. First, detach the audio (if it isn't already). Find some mark in the video (near the end that's out of sync) you know the sound will be immedieately identifiable. With the clip selected and the playhead to mark the start of the sound, type M to add a marker. Select the audio clip and find the sound that should start at the marker you just placed in the video clip; place the playhead and type M and add a marker to the audio clip. Command - R to Retime the audio clip and drag the retime bar until the markers line up (use the playhead as a guide.) Make sure Preserve Pitch is checked in the Retime menu.
HTH