Webpart not displaying sharepoint view properly

some background on my current issue:

1. I have created a Sharepoint list with two different views - All items view (as the name suggests, it shows all items in the Sharepoint list without filtering), as well as Management view (where I created the public view and applied certain filters to massage the data view and show by certain sales team only)
2. Separately, I have created a page and added a web part in the page to show the list (objective is to show Management View), and have set the view to "Management View" in the web part list settings
3. After saving my web part settings and republish my page, I can see from my end the web part is displaying correctly per my setting (i.e. the list web part is displaying Management View) - however when I share across the page link to my user (who have member privileges in my SP), they don't see what I see, but only see the web part showing All items view instead.

Any input or advice on this would be much appreciated, thanks!