Literal and straightforward. They are indeed cages, not tanks. Tuna don't swim through the gaps for the simple reason that they're too big to get through. Metal cages are used firstly because they're kept in the sea and you want the seawater to get in and out freely, and secondly because these fish are very big (commonly 250 kg or more) and very strong.

This is not about fish farming in the normal sense of the term. Bluefin tuna (atún rojo) is not reared in captivity; there are people working on it in Japan and the US, because it's the holy grail of fish farming, but they haven't achieved it yet, certainly not on a commercial basis. What they do is catch fully-grown bluefin in the wild with a net called a "cerco" in Spanish, transport them home in a transport cage and then put them in a fattening cage, also known as a farming cage.

So although it's not accurate to say that they are caught with a cage, they are caught as part of a process involving a cage: they're fished using a cage. This process is not illegal but the amount of tuna that may be caught this way is strictly controlled. The illegality is exceeding the quota.

"Cage" alone is not enough, because we ought to distinguish between the transport cage and the fattening cage.

"El suministro de atunes para su engorde en las granjas marinas depende directamente de la pesca de cerco. Se ha visto que las importaciones de atún rojo procedentes de las granjas han aumentado mientras que las capturas declaradas por los barcos cerqueros han disminuido. La única explicación a este hecho es la pesca ilegal, ya que la mayoría de atún de las granjas de engorde proviene de los cerqueros.
Según la FAO “desde 1996, el porcentaje de atún rojo para engorde se han incrementado continuamente, de forma que la mayor parte de los atunes capturados en el mediterráneo se destinan a jaulas de engorde.”"
http://www.andaluciaecologica.com/biodiversidad/atún-rojo/

"In the last 10 years, bluefin tuna fishing grounds have become highly profitable due to the big demand by the sushi and sashimi market. [...] In the last few years, the sharp rise in the fleet has been encouraged by the expansion of bluefin tuna fattening cages in the Mediterranean and the increase in the fleets' capacity."
http://oceana.org/en/eu/media-reports/features/bluefin-tuna

"Recommendation by ICCAT amending the recommendation by ICCAT to establish a multi-annual recovery plan for bluefin tuna in the Eastern Atlantic and Mediterranean [...]
j) "Caging" means the transfer of live bluefin tuna from the transport cage or trap to the farming cages. [...]
k) "Farming" means caging of bluefin tuna in farms and subsequent feeding aiming to fatten and increase their total biomass."
https://www.iccat.int/Documents/Recs/compendiopdf-e/2012-03-...

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Note added at 2 days38 mins (2014-12-17 12:59:02 GMT)
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By the way, Oliver's query made me look for an image of a "transport cage" for bluefin tuna, and it's actually a kind of net rather than what I'd call a cage. Here's another one:
http://www.gettyimages.es/detail/foto/bluefin-tuna-cage-bein...

The fattening/farming cages are probably the same. The word "cage" made me assume they'd be made of metal, but this is apparently not so.

By the way, ICCAT is the International Commission for the Conservation of Atlantic Tunas.