You can definitely use DA Search to search multiple tables at once. Here is how you should craft your results page.
First you should have one recordset per table. Start by crafting your recordset, then put the bindings for this recordset on the page where you would like to see them. Finally you will add a repeat region around the display bindings from the recordset, you can have it repeat for all entries.
Next you are ready to apply the first DataAssist Search server behavior to the page. Select your trigger, then the appropriate db, than add your search criteria. Just select the column to search, set the type to keyword then use the lightning bolt to select the value from your form. If your form is not on this page you may need to add to the bindings first by going to bindings > Form Data and selecting your search page.
Once you have completed this process for the first recordset test it to confirm that it is working correctly. Once you confirm that you can repeat these steps for each additional table/recordset you would like to search through.