For analysis, I cut your tempos to 1/3 and converted your quintuplet notes to tied 64ths. Your left hand quarter notes in bar 2 are correctly placed, both aurally and visually.
To get the right playback, mute the left hand part, copy it to a new staff, and tie the quarter notes in bar 2 to the sixteenths. This will give you the playback you want. Make this "playback" staff invisible.
Right hand part:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Tempo|Tempo:40|Pos:34|Visibility:Never
|Key|Signature:Bb
|TimeSig|Signature:Common
|Note|Dur:8th|Pos:-3|Opts:Stem=Up,Beam=First
|Note|Dur:8th|Pos:-6|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:-3|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:-6|Opts:Stem=Up,Beam=End
|Note|Dur:8th|Pos:-1|Opts:Stem=Up,Beam=First
|Note|Dur:8th|Pos:-3|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:1|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:-1|Opts:Stem=Up,Beam=End
|Bar
|Tempo|Tempo:50|Pos:30|Visibility:Never
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam=First
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:5|Opts:Stem=Down,Beam
|Text|Text:"5"|Font:StaffItalic|Pos:-9
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:3|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4^|Opts:Stem=Down,Beam
|Note|Dur:64th|Pos:4|Opts:Stem=Down,Beam=End
|Tempo|Tempo:40|Pos:34|Visibility:Never
|Note|Dur:8th|Pos:1|Opts:Stem=Up,Beam=First
|Note|Dur:8th|Pos:-1|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:-3|Opts:Stem=Up,Beam
|Note|Dur:8th|Pos:-1|Opts:Stem=Up,Beam=End
|Bar
!NoteWorthyComposerClip-End
Hidden staff:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Bass
|Key|Signature:Bb
|TimeSig|Signature:Common
|Note|Dur:4th|Pos:-5
|Note|Dur:4th|Pos:-1
|Note|Dur:4th|Pos:-5
|Note|Dur:4th|Pos:-1
|Bar
|Note|Dur:4th|Pos:-4^
|Note|Dur:16th|Pos:-4|Visibility:Never
|Note|Dur:4th|Pos:-1^
|Note|Dur:16th|Pos:-1|Opts:Muted|Visibility:Never
|Note|Dur:4th|Pos:-5
|Note|Dur:4th|Pos:-1
|Bar
!NoteWorthyComposerClip-End