As far as I know, the only way to ensure this works is to have your Seeder also know Mean Look. Mean Look would trap the enemy Pokemon for as long as the user is on the field. Even on the turn you switch to your Shadow Tag Pokemon, your opponent would be unable to perform the switch. Th e only Pokemon capable of learning both moves is the Snivy line.
Addressing your specific concern.... I THINK it occurs in Speed order. The faster Pokemon would be switched first. However, I don't think Shadow Tag comes into effect on the turn of the switch, but rather is applied between turns.