This very same problem has been discussed here:
In this thread someone made the suggestion of actually recording the sound of keys pressed on the keyboard at the same time with the MIDI (with no output instrument attached). So the OP in this thread did exactly this and came up with definite proof of what we’ve been suspecting (and possibly blaming on our own inaccurate playing) for a long time:
MIDI IS ALWAYS RECORDED TOO EARLY.
You ALWAYS need to move recorded MIDI parts forward. This may be worse with long latencies, but it is still recognizable even with very small latencies.
So, the time when you push a key (as compared to either playback or a metronome) should be recorded. Period. This would be expected behaviour by anyone. We are not talking about intuitive compensation for delayed instrument playback (because there is no output instrument selected).
So, if for some reason, placing whatever you record EARLIER than when the key was actually pushed would be “expected” behaviour (which I fail to see), then you would also expect AUDIO to behave in the same way. So at least, when you record MIDI and audio at the same time, they would also be in the same place, regardless of latency.
This experiment finally (after several years) proves that the Cubase behaviour of ALWAYS placing recorded MIDI EARLIER than the actual point of pushing the key is a BUG. A rather annoying bug that should be addressed as soon as possible.
Other DAWs do not seem to show this behaviour (could someone run the same test on Logic or Reaper?)
BTW: This has nothing to do with any kind of quantising whatsoever. Imagine playing to an audio click without any grid. The erratic behaviour would persist. And no, the quantise feature is not designed to move everything forward.