Yes, make sure you have the setting correct. Go to Settings > New Keyword: Suggest new Keywords only.
If you decide to keep your current account structure, you can manually synchronise keywords from the automatic campaign to the manual campaign via Adspert’s dashboard.
Adspert will suggest those keywords to the best matching (manual) campaigns. You can find the suggested keywords under the page “Keywords Suggestions”.
For more details what Adspert takes into account to suggest new keywords, have a look at this article: How does Adspert decide which Keywords to add to my manual campaigns?
Adspert will not create manual campaigns, nor will it sync keywords automatically if your Keyword Addition setting is set to “Suggest New Keywords only”.