we use it in one of our projects. Developed with Eclipse. Part of a .war in Tomcat. There is a tutorial which can get you started. Collegue has developed that part and it doesn't look that dificult. There is lots of documentation with quartz including tutorials. You might start there, if you not allready have done that. Some objects are just scheduler triggered/managed and not by incoming http-request. Its a bit annoying to debug, because of time trigger, but thats all.
You might ask in different forum, because quartz has nothing to do with web application frameworks.