This whole idea is interesting. My father z"l didn't have this minhag, but my in-laws do, and my wife insisted that we follow along. I usually give the Rav two checks when I sell chometz one for him, and one for Maos Chitim. I also generally don't share the amount I give with others for a lot of reasons.
I often wondered about how this evolved. In my limited anecdotal evidence, I think it has to do with the financial model of your shul (or of the shul the family member you inherited this minhag from)
Most shuls have one of two models:
- A membership model where you pay one big membership dues per year that covers all costs of the shul
- A pay-for-play model (for lack of a better term) - where you pay a small or no membership fee, but every little thing has a dollar value - i.e. aliyah auctions etc.
in the former, especially in a large shul, I would image tipping the Rav is a lot less prevalent, because the Rav is drawing a decent salary, and it's likely that the shtellar is a his main parnash.
in the latter, especially if it's a shtieble, I think people are more inclined to give, as every little dollar goes to help the Rav and/or Bedek habayis.