As soon as an order is placed Shopify notifies both Store Pickup + Delivery (SPD) and Order Tagger. Order Tagger immediately follows your configured rules and updates your orders tags. At the exact same time Store Pickup + Delivery would also be processing the order and adding it's tags. As neither app is aware of the other this can lead to missing tags.
If you wish to continue using Order Tagger you must disable all tags within SPD and instead create additional rules within Order Tagger.
You can do this by creating rules based upon the order attributes as shown below.