Looks like a small bug in the new tie function.
Try using layered staffs as a workaround. Your first staff will be modified to take out the two ties you mentioned:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Key|Signature:Bb,Eb
|TimeSig|Signature:4/4
|Dynamic|Style:mf|Pos:-9
|Note|Dur:Half,Dotted|Pos:2
|Note|Dur:16th|Pos:1|Opts:Stem=Down,Beam=First
|Note|Dur:16th|Pos:2|Opts:Stem=Down,Beam
|Chord|Dur:8th|Pos:0^,4^|Opts:Stem=Down,Beam=End
|Text|Text:"47"|Font:StaffBold|Pos:10|Justify:Center|Placement:AtNextNote
|Bar
|Chord|Dur:8th|Pos:0|Opts:Stem=Down,Beam=First|Dur2:4th|Pos2:4
|Note|Dur:8th|Pos:-1|Opts:Stem=Down,Beam=End
|Note|Dur:8th,Grace,Slur|Pos:1
|Note|Dur:8th,Grace|Pos:2|Opts:Muted|Visibility:Never
|Chord|Dur:8th|Pos:2|Opts:Stem=Up,Beam=First|Dur2:4th|Pos2:-3
|Note|Dur:8th|Pos:0|Opts:Stem=Up,Beam=End,Tie=Downward
|Chord|Dur:4th|Pos:b-1|Opts:Stem=Down|Dur2:Half|Pos2:0
|Note|Dur:8th|Pos:-3|Opts:Stem=Down,Beam=First
|Note|Dur:8th|Pos:-5|Opts:Stem=Down,Beam=End
|Text|Text:"48"|Font:StaffBold|Pos:10|Justify:Center|Placement:AtNextNote
|Bar
|Rest|Dur:8th,Dotted
|Note|Dur:16th|Pos:-3
|Note|Dur:16th|Pos:-2|Opts:Stem=Up,Beam=First
|Note|Dur:8th|Pos:0|Opts:Stem=Up,Beam
|Note|Dur:16th|Pos:0|Opts:Stem=Up,Beam=End,Tie=Downward
|Chord|Dur:4th|Pos:0|Opts:Stem=Up|Dur2:4th,Dotted|Pos2:-6,#-3
|Note|Dur:8th|Pos:0|Opts:Stem=Up,Beam=First
|Chord|Dur:8th|Pos:0^|Opts:Stem=Up,Beam=End|Dur2:8th|Pos2:-7^,n-3^
|Bar
|Chord|Dur:4th|Pos:|Dur2:4th|Pos2:0
|Note|Dur:8th,Grace,Slur|Pos:4
|Chord|Dur:8th|Pos:5,7|Opts:Stem=Down,Beam=First
|Note|Dur:8th,Grace,Slur|Pos:4
|Chord|Dur:8th|Pos:5^,7^|Opts:Stem=Down,Beam=End
|Chord|Dur:4th|Pos:5,7
|Note|Dur:8th|Pos:7|Opts:Stem=Down,Beam=First
|Note|Dur:8th,Grace,Slur|Pos:4
|Chord|Dur:8th|Pos:5,7|Opts:Stem=Down,Beam=End
|Bar
!NoteWorthyComposerClip-End
Then your second staff is just:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble|Visibility:Never
|Key|Signature:Bb,Eb|Visibility:Never
|TimeSig|Signature:4/4|Visibility:Never
|Dynamic|Style:mf|Pos:-9|Visibility:Never
|Rest|Dur:Whole|Visibility:Never
|Bar|Visibility:Never
|Rest|Dur:4th|Visibility:Never
|Note|Dur:8th|Pos:2|Opts:Stem=Down,StemLength=0,Beam=First
|Note|Dur:8th|Pos:0^|Opts:Stem=Down,StemLength=0,Beam=End,Tie=Upward
|Chord|Dur:4th|Pos:b-1|Opts:Stem=Down|Dur2:Half|Pos2:0
|Rest|Dur:4th|Opts:Stem=Down|Visibility:Never
|Text|Text:"48"|Font:StaffBold|Pos:10|Justify:Center|Placement:AtNextNote|Visibility:Never
|Bar|Visibility:Never
|Rest|Dur:4th|Visibility:Never
|Rest|Dur:8th,Dotted|Visibility:Never
|Note|Dur:16th|Pos:0^|Opts:Stem=Down,StemLength=0,Tie=Upward
|Chord|Dur:4th|Pos:0|Opts:Stem=Up|Dur2:4th,Dotted|Pos2:-6,#-3
|Rest|Dur:4th|Visibility:Never
|Bar|Visibility:Never
|Rest|Dur:Whole|Visibility:Never
|Bar|Visibility:Never
!NoteWorthyComposerClip-End
You can see I've reversed the stem directions of the offending notes in the bottom staff, and given them a stem length of zero.