The bladebound magus says the following
Languages and Skills: A black blade starts with Common as a language. As the black blade increases in Intelligence, it manifests knowledge of languages and arcane lore. Upon reaching an Intelligence of 12, it gains a bonus language of the GM’s choice, and gains 1 rank in Knowledge (arcana). Each time the sword gains a bonus to Intelligence, it gains another language and another rank in Knowledge (arcana).
As written, that should mean a blackblade with a 16 Intelligence should have 5 ranks and 5 extra languages. However, that doesn't seem what the designer intended. It seems like they intended the blackblade to receive a bonus language and skill rank whenever their Intelligence modifier increases, similar to a normal character.
I think the way it is written is a mistake and it should be whenever the modifier increases, as you say.
That seems logical, that 'gain a bonus to intelligence' was meant to read as 'gain a point of intelligence bonus'. Not that it would be broken to allow a 13th level character's sword 5 ranks in a knowledge and 5 languages rather than 3 and 3.