Google-chrome – Why does Chrome remove extension’s icon when in ‘incognito mode’

It would appear you are running into the intended feature of the omnibox, it will give you auto-suggestions pulled from the internet as you type.

If you start typing 'superu' it may bring up superuser.com even if you have never been here before. this is not instant search as you mention you do not have enabled, instant search is an extension of this where it will actually load the best result, aka your feeling lucky, as you type. with instant search enabled it would already be loading superuser.com if you started typing it and it was the best result based on google magic.

Turning off Auto-Suggestions

1. Clear your browsing history

2. Click the Tools menu

3. Select Options

4. Click the Under the Hood tab and find the ''Privacy section

5. Deselect the 'Use a suggestion service to help complete searches and URLs typed in the address bar' checkbox.

6. Click Close.

referance: http://productforums.google.com/forum/#!msg/chrome/0DR-pLIVI5g/XuqF5qasts8J

I have solved this problem by writing a small tampermonkey script, which will redirect your search request from google to duckduckgo, if it detects that you are using incognito mode. (I tested it with Chrome 75.0.3770.142 on Linux)

Script: https://greasyfork.org/en/scripts/388055-redirect-google-search-requests-to-duckduckgo-incognito-only

However, it is more of a workaround than a solution.