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It depends on the address, In the case of "XRP" currency. The reason why the exchange knows the address is coming from gambling activity because the address is already have a custom name "STAKE" so they are really easy to be recognized.
IMO, even the exchange has a policy they can't accept any fund from gambling activity as long there is no information who mention about gambling activity like the name of the casino or maybe some memo on the chain.
I also presume on this one unless if the said local wallet provider do make out some in depth search on each addresses on where it do came from and its just not surprising that they would really be listing
out to those known gambling sites address but I don't see for it to be that much effective since there are sites do give out dynamic addresses which its really hard to determine if you are really passing
off funds to gambling site.
For people who had been using this wallet then you should be aware on possible problems if you do try to violate.