Here is a step by step guide on how to Import assets from Curator into your Adobe project.
Curator sub-clips can be imported into Premiere Pro.
Curator sub-clips cannot be imported into After Effects
Collections can be imported as described in this article and can be imported in the same order they were sorted in (Premiere Pro only) depending on how import preferences are set up.
Importing Assets
Navigate and select an asset(s) or collection as per Adobe panel explained
From here:
A) Selecting the Import menu itself will action the default type as per Import Preferences:

B) Selecting the arrow to the right of the menu will allow you to bypass the default type and select to import as either Proxy (lo-res) or Hi-res (default secondary option).
There may be multiple options to select here as configured by your system administrator. The options here will differ depending on the transcode settings and formats of the asset that are available:
Your asset(s) will be placed in your adobe project.