phals naturally bloom during the winter, so they will stay quiescent for a while. the action will start in december!
if you want, you can leave the stems (commonly known as spikes) as they are. since they're still green, they have a chance of "activating" during the winter and producing more buds. if you cut them, make sure you use sterile equipment - disinfect with alcohol, bleach, or running them through an open flame. cut right above a node/bract. some people like to put cinnamon on the cut spikes, probably to encourage desiccation of the spike and prevent fungal/bacterial growth (it's essential a cheaper fungicide). i don't think it's necessary to put anything at all if you don't want to. in the winter (december or maybe january of next year), a new spike will start to grow from the base of the plant!