If the address you entered was correct, you should open a support ticket with the exchange after a reasonable period of time. Check the transaction ID in https://primestats.info/ to verify.
Web wallets present unique security challenges and are not recommend. Any cryptocurrency exchange that supports SiaPrime will give you SiaPrime addresses and allow you to send and receive SiaPrime. This is not a “true” web wallet in the sense that the exchange controls the private key and thus ultimately controls your SiaPrime. So as a matter of good practice, of course, the suggestion is only send what you need to, to an exchange and keep the rest in your wallet.
Large exchanges have steep listing fees and minimum volume requirements. Being listed on large exchanges is highly requested and will come with time as community support and network use grows.