In EOS, will the voter get money if its voted node becomes the proposer?
Also, how is the proposer itself rewarded?
No. (To correct your terminology slightly, "will a token holder receive any reward if a block producer candidate for whom they vote succeeds in being elected to make blocks as an active producer?")
Not only will the system not automatically reward any voter for voting for a candidate who is elected to be active, the Ricardian contract for the voteproducer
command currently says:
I stipulate I have not and will not accept anything
of value in exchange for these votes, on penalty of
confiscation of these tokens, and other penalties.
This means that if you were to be rewarded manually, say by the producer candidate for whom you voted, you could be in serious trouble.
source: https://github.com/EOSIO/eos/blob/master/contracts/eosio.system/eosio.system.voteproducer-rc.md