That's not a privacy issue. But indeed, you will support Microsoft when using DuckDuckGo. I believe it's necessary to use a big search engine before building your own.

Their ads also run via Bing Ads. This is something they really should change a believe. I tried to run ads for Simple Analytics on DDG but it feels very wrong to use Bing Ads for that. You can't also select "Run on DuckDuckGo only". I think they should move to something of themselves which is likely to happen if they grow bigger.