Packets are how the game functions in communication with the server. Some of these are set as traps which ban your account for a certain amount of time.
Simply logging into a trainer such as Dark Mystic, wouldn't get you banned - the likelihood is that you either used an outdated function which activated one of these packets, or clicked on the '7 Day Ban' option available on some trainers.
This is basically what LM was saying
In future, I think it would be better to use 'trainer' to talk about the application e.g Le Bot and 'bot' to talk about the individual tasks e.g Arcangrove Rep.
Not that it matters, or that one is more correct than the other, but it just helps save confusion.