You kind of have to have the server doing the collapse anyway, or clients can cheat by biasing the collapse towards tiles that are beneficial to them in some way.

You can partially work around this by requiring the client to use a server-provided PRNG seed, although even then a kind of aim bot could help the player decide which path to explore to get favourable tiles.

So your best bet to avoid cheating is to do the collapse on the server using a hidden RNG.