You still does'nt show a track where one note is ahead and next note is after beat in different intervals (Free Running), and where you show/ tell what is Legato style played trigger notes and what's not.
Your also does'nt tell your Sync note settings for both Pigments and Omnisphere.
Did you try the BPM setting for Rate that i suggested?
If you use BPM Rate, then the first note you play any time after playing no notes will be "Instant". "Free running".
If your 1/16 notes are played excact like you show and they are'nt synced at all, then this is the setting to use, but only when not playing Legato style, as the seq/ arp will continue playing just like it look like it does in your screenshot.
I would also like to have the option to have legato played note to play instantly too. That would be no sync at all except between manually triggered notes.
However if you actually wan't a sync to ie the nearest 1/16 note, then Pigments sequence have to run at 1/16 note Sync Rate.
It can be the case you have this for the Omnisphere examples you show but not for Pigments. You does'nt tell.
But if you in example have a Sequence set to 1/4 Sync Rate in Pigments, then you in example unfortunately can't have it playing 1/16 or 1/8 ahead or after beat while the host is running, if that's what you wan't. It will be 1/4 note synced.
In this case you can set the the Seq Rate to BPM with a value 25% of the hosts BPM. This will give 1/4 notes for each seq step, - but everything will be free running.
In standalone mode or when a host is'nt running, then Pigments start playing a seq as soon as you play a initial note no matter the rate setting. This option would as said be nice to have when the host is running as well. Is that what Omnisphere does? I'm not sure if this is a bug in Pigments or perhaps a missing feature. I do think it's strange a sequence set to 1/4 note sync in example can't start at a 1/8 note. That said, then it can make sense a incomming note is quantized but not a recorded note. An option would be good to have.
I would also have the option to let manually played Legato style notes to trigger in all cases.
Pigments does'nt have the Song Position mode Omnisphere has, as i wrote and posted a video example about. It could be great if Pigments had this too.
This is what Omnisphere say in their manual:
https://support.spectrasonics.net/manual/Omnisphere2/25/en/topic/trigger