Those bottles already have that deposit on them in New York State. I regularly see tons of people going around Buffalo picking up bottles and cans to take back to redemption centers for the deposit. All that plastic in the river is happening in spite of that 5 cent redemption.
Now this part is just an anecdote but the people I personally see most often chucking their bottles on the ground are Canadians tossing them out their car windows. Which makes sense since you can’t take them back across the border with you and still get the deposit back. They’d have to do it before heading back to Canada.