your question isnt very clear but no the bot doesnt stop after it dies, set your home point at an aether in the same map your grinding and when you die youll be in the same map you wer and the bot will continue. there is usually a break after death and the bot will usually wait for a non blacklisted fate. autostart is a feature to start the bot on the last mode it was in when once it finishes loading after its injected. (mainly for use with the gui launcher which isnt recomended atm)
edit: also make sure you set the evac spot under the grind drop window in ffxivminion
edit: also make sure you set the evac spot under the grind drop window in ffxivminion