Learn English – Expressions to describe having immediately understood someone’s personality

The phrase in your question is good:

The issue only occurs at the turn of the year

(if it only happens at the moment the year changes), or perhaps

The issue only occurs around the turn of the year

(if it happens for a longer time period)

Or you can paraphrase:

The issue only happens when the year changes from 2010 to 2011

(though that might imply it only happened in those specific years), or

The issue only happens in the first few (hours, days) of January

The phrase bait and switch is often used to describe a process in which an attractive product is offered to induce buyers, and once they engage with the salesperson, they are diverted to a different, more expensive product, usually being told that the original is not available or otherwise undesirable.

The term is also applied to politics and other dealings in which an innocuous proposal is deceptively introduced, only to be substantially changed (as was the original intention) to something much more controversial.