Welcome to the Monday community!
It seems like this is pulling up as intended in Monday. It has nothing to do with using the Tag column, but this is how search results populate when you use the “Search Everything” button on the bottom left in Monday. Its pulling all items on your entire Monday account(that you have access to) and putting them into one view.
If these items are all in the same board, then I would instead use the search feature at the top of the board and see if that works better for you.
If you search for the tag, it will only pull up the items who have subitems with that tag, and when you open the subitems, it should only show those with the tag. You can also see which group they are in when you search like this.
You could take this a step further. If you click the settings arrow of your Tag Column, you can choose to “Show summary on Parent Item”. This will push all the tags up to your parent item into on column that looks like a Mirror column. If you do this, then you can use the “Filter” feature and save custom filters for specific projects if you think you will be constantly searching for that tag, it might save some time in the long run. To use the Filter in this way, it will require that you “Show Summary on Parent Item” because currently Filter does not support subitems.