The host view phase is applied to the link
With the default By Host View display, a link has no phase settings of its own in your views. A plan set to the Existing phase with a Show Previous + Demo filter shows the link through that same phase and filter, after mapping. This is why the same link looks different in your existing and new construction plans.
Check the Phase and Phase Filter properties of the host view first. If they are right for your own model but wrong for the link, fix the phase mapping of the link type or override the display for that link in this view.
Temporarily set the view phase filter to Show All. If the missing linked elements appear, the issue is phase related.