I also find that (maybe because my PC is a bit older..at least 6 yrs old... but I7 with 32gb memory) that the video lags sometimes and is not always accurate. It may sync a bit different in the render.

It syncs exactly as you sync it, it just doesn't preview correctly. You always want to test render. I have a media player and a bluray that plays from a USB drive that I always watch to make final tweaks and adjustments. I don't worry so much about exact frames as I do how it looks in realtime trying to keep an eye as if I had not seen it before. Usually my wife gives me good input as well.

It's great fun! I use Marker generation as my primary Grid mapping for creating cut splits.

OK, 2 tips:

1/- Slow down the Preview playback. This will get you real close.

2/- Use the M Marker key to tap out the beat. Then use the Build RAM Preview often! I have a MACRO and have set this "Control" set to my Control Shuttle Pro.

The free Timeline Tools had added a Marker to Beat tool that I found useful. It has sensitivity and spread options.

You might want to experiment switching Quantize to Frames ON or maybe OFF.

You can cut at video frame boundaries; or you can ungroup the audio, turn off quantize temporarily, and make more precise audio cuts without disturbing the video. .

You cannot divide a video frame, and doing so on the timeline will give unintended results.

For whatever this is worth there's an old rule of thumb in animation, established decades ago by the old Disney animators, which is to make lipsynching work the best, make the image track lag behind the sound track by 2 or 3 frames to best achieve the perception of perfect synchronization. Perhaps this is why your client perceived the real sync to not be accurate. Worth the try, though animation may be a lot different than live action.