1. Yes, what you were doing is in violation of Nevada Law.
2. The Cashier, when advising you of that, should have done something other than just give the tickets back to you. I do not know what the Casino's policy is on that, however, to advise you that it is against the law and then give them back without follow-up instruction just can't be a proper course of action.
3. However, at that point, the tickets should have been turned in to Security, as opposed to some of them being cashed out/played.
4. So, are we really taking about .38c? If I read your post correctly, the biggest voucher was .39c, meaning that overall, the total of vouchers that belong to others was certainly greater than .38c. (Perhaps you crossed a threshold in aggragate. )
5. As for an apology from the Casino, don't look for that, nor should one be offered. In fact, if you look around any casino in Nevada, you will see signage that states that a Casino employee has powers of detention, until arrival of uniformed officers if a they believe a crime is being committed. If they really wanted to put the screws to you, they could have, and they probably had the evidence on video.
6. Talk to the Manager? Yes, but only if to apologize for your initial action (Buffaloing or whatever it's called) and to advise that it will not happen again, and also, to point out that the Cashier did not act in a manner that was consistent with the Law, which was confusing and exacerbated your follow-on action.

Well, as I said, FWIW, that's my opinion.

Jim