The rate limits are applied on a per-connection basis; not per-account, or per-ip. The way large bots get around rate limiting is by spawning more connections. That is to say, if you had two connections to twitch’s chat servers, and the first one sends 100 messages to a stream’s chat, you could use the 2nd connection to send another 100 messages within the same 30 second time period.
The reason large bots often have multiple IPs is their developers make use of cluster computing to spread the bot across multiple hosting services to ensure uptime and such