I walked the CF from mid-May to the end of June. The weather was not what I expected. Icy, cold, mud, The route Napolean was closed due to bad weather. You can see from my avatar that I've got my rain jacket around my waist, I'm wearing a fleece pullover, and layers underneath. I didn't buy them along the way, but I wished I had had a pair of gloves during those first two weeks. Who knew Spain in May would be like that! On the other hand, once the rain stopped, about halfway, it never returned. Not a drop in Galicia - thank you, St. James!!
You should consider preparing for all weather and plan to bring efficient layers, including sleepwear.
The blog of my trip covers that time frame, including my prep.
PS - Definitely suggest a rain jacket rather than a poncho. It was much easier to get into and out of on short notice, kept me very dry, and served double duty as a windbreaker. It was lightweight but sturdy (I've used it for more than ten years now) and fit easily into my pack. It is from EMS.