Here's the basic rule: did you approach the lawyer in a professional capacity in order to obtain legal advice? If you did, the conversations are privileged. If you merely chatted with someone who happened to be a lawyer, the conversation is not privileged.
The symbolic payment of $1 is one way of establishing by a physical act how both parties view the conversation. But confidentiality does not depend on the payment of a dollar or for that matter, any other amount. There is no magic about a one dollar bill. The risk is that the amount is so low it may be characterized as trivial.
If you wrote out a check for $500 for a "consultation," it would be difficult for a lawyer to claim--especially if he cashed the check--that there was no privileged conversation. "Yeah, he gave me a dollar. I thought it was to tip the barista." If you don't have cash, a transfer of at least $100 is decent evidence that you, as client, were engaging in what you thought were privileged conversations.
A common tactic in some places is to visit several lawyers or law firms so that they get "conflicted out," that is, they cannot represent your opponent. This is common in divorce practice and is the reason that most matrimonial lawyers will not talk to clients unless they are paid an initial consultation fee of $500. There are exceptions to the rule. If you ask the lawyer for ways to break the law or tell him that you are planning a crime, or invite him to participate in criminal activity, these conversations are not privileged.
