1. What does it mean?
Wordplay combining 돈 ('money') with 혼쭐, as in giving someone a hard time. The meaning is flipped into a positive joke: customers 'punish' a deserving shop with purchases and an enthusiastic show of support.
Also written or said as 돈쭐내다, 돈쭐 내다
2. The nuance
The usual expression is 돈쭐 내다. Despite the mock-threatening wording, it describes voluntary support, not a fine or a demand for money. The label itself does not verify a business's story.
3. Examples
“동네 행사에 음식을 나눠 줬다길래 가게에 돈쭐 내러 갔어.”
I heard they gave out food at a neighborhood event, so I went to support the shop with a purchase.
“좋은 일을 한 가게라면 돈쭐로 응원하고 싶어.”
If a shop has done something good, I'd like to show my support by shopping there.
Sources
Korea Housing Finance Corporation: Korean slang guide
References support the meaning and usage. Example sentences are written for NoCapWiki.