First of all posts about this have been made already and people discussed it in the past. For reference I take the following posts and discussions:
http://forum.square-enix.com/ffxiv/t...Penalty-Policy
http://forum.square-enix.com/ffxiv/t...l-reason-given
http://support.na.square-enix.com/ru...2&tag=users_en
https://gamefaqs.gamespot.com/boards...7060061?page=1
https://steamcommunity.com/app/39210...5556492588920/

I will try to talk about the points in discussion separately, them being the age of 13 and cusswords, the usage of the warning system for offenses and the lack of information for the offender.

For the first point, given that the game is for the age of 13 and older according to the ToS, and includes itself a filter for cusswords, I do believe that this penalty is not really related to this possible situation. The removal of that filter and exposure to such content is in the hands of the player and therefore the system allows the player to be responsible for that exposure. That said, many people comment on how the game itself uses cusswords occasionally for the scenario and quests in the text, something I'm personally unable to recall aside of some friendly variants based on the regional differences of each region, as how lominsans would use different terms than gridanians. Still, given that the ToS include this specific paragraph for their point 3.3, it is surprising that the rules have not been updated whilst the steam page for instance shows it to be a game for 16+, probably because of the content. Said rules are on a previously linked page with last update being on 2013, so if I'm wrong on this part I'd appreciate to be let known. In any case I do consider that the exposure to possible profanity is in the hands of the player.

About the offense system, I haven't found anything that shows how to differenciate an offense worth a warning and a caution. I faintly remember a possibly year old Live Letter that addressed this, but in any case, it does not explain which offenses are to be considered a warning or a caution in such an ambiguous scenario. For instance, the usage of profanities during a heated argument (not directed insults) are worthy of a caution or already a warning? When does a caution stop being one and becoming a warning? Obviously direct insults and attacks are to be treated with higher care for they mean to directly harass a player instead. I do believe that in cases a player is becoming directly target of rage and insults a warning could be issued, but that just leaves it as a matter to discuss and always in an ambiguous zone, given that other cases such as the one in the steam link have received bans for this reason, while in my case it was a mere warning.