Quantizing already quantized notes leads to a dark portal of mysteries and small voltage offsets.
Add a small +- voltage offset to your input cv and your half step off will be fixed, or migrate.
Depends on how your quantizer rounds up or down when the input is close to a note.
The notes from the sequencer are not already quantized. Its a digital sequencer so the voltages are just precise.
So the fact that just the first note is getting shifted up a semi tone really makes little sense to me.
But I don't build or design modules so thats not much of a surprise.
I have repeated the experiment but instead of using the built in quantizer I used an external one and the sequence plays as expected.
So it does appear to point to some issue with the internal quantizer to me.