Hi Mirko!
I’m not sure that’s our issue, since some tags are searchable on our site already. For example, the recent product tagged with “bike” and “test” will show up if I search “bike” but not if I search “test”. If I search any tags that are attached to the very first batch of products I imported, too, those also bring up results from that batch.
I tried installing one of the search plugins just to check, but it didn’t cause any changes.