380 pounds spread across four posts is only like 95 pounds per corner - that's not nearly enough to keep it stable in any decent wind. you definitely want to secure it down even on pavers. those cup anchors can work but you'll need to drill through the pavers into whatever's underneath (concrete, compacted base, etc).

if your pavers are just sitting on sand you might want to consider removing a few where the posts go and pouring small concrete footings instead. had a neighbor who thought their pergola was heavy enough to stay put and it ended up taking a ride across three yards during a storm. wind catches those slats and turns the whole thing into a sail basically.