Just buy a stans no tubes refill bottle. 2 oz. Then keep refilling the sucker. Remove the valve core. If you're doing it the old school way it's way messier. The stans no tubes syringe was even messier.
I always seat tires before putting sealant in and this almost guarantees no splash back. https://sprocketkings.com/products/stans-no-tubes-regular-tire-sealant-2oz-bottles
Just like the device in the article it's fitted around the valve and the sealant goes everywhere. At least the stans syringe was over valve.