I'm not positive, but I do not recall fusels being one of the issues (e.g., diacetyl, green-apple) that occur in every beer, and if allowed time, the yeast self-clean. Most sources say fusels rarely diminish [much] over time. The delay in your detection of the fusels could be that other "green beer" flavors mask them until later.
The transition from wort to beer is quite complicated, and takes longer than many sources may quote, esp. recipe kits that recommend "one week primary, secondary, then package" types of timelines.
So prevention is the only solution, and fermentation temperature control, pitching big healthy yeast starters, and wort aeration would each help produce cleaner fermentations. If you don't have a freezer, nor room for one, then you could try the water bath, wet t-shirts, and fans that some use, and also the big starters and oxygen to alleviate yeast stress wherever possible.