The STAR rebate checks are a new thing, that is, checks sent to new buyers. People who bought years ago just get the STAR rebate automatically on their school tax bill. I'm not sure if you will eventually switch to that, or the rebate checks after paying the taxes is the new norm.
The other rebate checks are more random. At any given time there are a few different ones, and I'm never quite sure which is which or when to expect them. I'd guess that's by design - we view them as a nice perk, but can't rely on them because they are so random.
However, anyone that works for any municipal sort of entity always has those tax cap rules hanging over their heads. The state uses the carrot of tax payer rebate checks for your community members to force down inflation increases in budgets of all kinds : volunteer fire companies, libraries, schools, village/town/etc governments, parks, etc. If any agency busts the cap, no rebate checks are sent to that community (the stick). So there's a strong incentive to stay under the cap. Unfortunately, the state sets the cap each year: inflation (as defined by the state), or 2%, whichever is LESS. For several years recently, inflation was set at .75%. The library I work for did not pursue any budget increases in those years, because the cap limit was less than the cost of complying with holding a vote to increase our budget! The inflation rate was finally recognized as >2% this year, but we were still capped at 2% increase (our last increase was in 2012). Meanwhile, the state increases in minimum wage will eat up the budget increase. Staff shouldn't be making minimum, but tight capped budgets constrained raises. And then Cuomo cuts state library and school budget aid below legal limits, and every year there's a fight to restore library and school funding.
Sorry for devolving into a rant - it just gets old after a while. Yes, state income and property and sales taxes need to go lower, but there's no fat to cut in library budgets or rural schools or village government. Try Albany itself.