If you have a tags database, then you can't use and select natural Notion tags, you need to relate the tags database with your notes database to then select from that relation a tag. This way it will work as you need.
Keep in mind it does not go to the tag database when you select one, it is only a reference and a relation between the 2 databases, so the item exists in both. After this you can create views and filters to present the information as needed, for example by tag.
Another thing is that there is only 1 tags database, so if you create a new note and the tag does not exist, you just create it on the fly and it will be added to the tags database.
I suggest that you have a look at some Notion relations tutorials to understand better how this works. Once you click with this, it changes completely the way you will use Notion and you will like it even more.
Hope that helps.