I agree with you, ageing or seasoning do not sound right. Stagionatura here means that you can bake/cook this food and eat it straight away ... I would not use ageing. Stagionatura is used when you write about wine or cheese. It is a long process. I hope this helps.

seasoning is fine but the other terms are also used.

I think this just reoterates the fact that for these cakes you don't need to let time pass before you serve them.

see
Care and Feeding a Fruitcake - Pressure Cooker Recipes
missvickie.com/recipes/desserts/fruitcake-carefeed.html
A fruitcake needs care and feeding for a period of time as it ripens and matures. ... Aging is sometimes called 'ripening', and allows the ingredients in the ...

Do I need to season my fruitcake? What does that even ...
blogs.edmontonjournal.com › Blogs › Life › Atco Blue Flame Kitchen
Dec 3, 2013 - Answer: “Seasoning,” or ripening, a fruitcake involves letting it ... the fruitcake wasn't formulated to survive the room-temperature aging period.

Do I need to season my fruitcake? - ATCO Blue Flame Kitchen
www.atcoblueflamekitchen.com/.../Do-I-need-to-season-my-fru...
​“Seasoning,” or ripening, a fruitcake involves letting it mature in a cool, dark place for several weeks. While different recipes call for different processes, the ...

assuming it's about making the cakes/breads:
Bake for 1 hour 40 minutes, then leave to cool completely in the tin. Once cool, take out of the tin, wrap with baking parchment then foil, before stashing it away in its cake tin or other airtight container. Though, unlike a traditional fruit cake, it doesn’t need to stand before being divinely edible.

http://www.nigella.com/recipes/view/gorgeously-golden-fruit-...

Carrot and Banana Cake - Farrington Oils
www.farrington-oils.co.uk/assets/Recipe.../Recipe-card-Carr...
Turn the mixture into the cake tin and bake for 1 hour. Allow to stand for 10 minutes before turning out onto a cooling rack. Blend all the topping ingredients ...

Thanks again for tasty recipes. Oh and BTW its very moist and the cake doesn’t need to stand in the fridge very long for it to be perfect.
http://www.olgasflavorfactory.com/favorites/raspberry-piece-...

Morrisons: Wright's Chocolate Fudge Cake Mix 500g ...
groceries.morrisons.com/webshop/product/...Cake-Mix/113041011?...
A rich Chocolate Fudge cake mix with a melting chocolate crumb. ... Remove from oven & allow to stand for 10-15 minutes before tipping out onto a cooling wire.
APPLE AND DATE CAKE | Recipes | Nigella Lawson
www.nigella.com/recipes/view/apple-and-date-cake-523
Method. Place apples, dates and soda in a bowl. Pour over boiling water. Allow to stand until cool. Beat butter and sugar together in another bowl until thick and ...

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Note added at 14 hrs (2015-02-17 22:27:37 GMT)
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I don't know of any breads or most cakes, apart from Xmas/some fruit cakes, that need maturing or ageing, etc.