What triggers the INTACT PTH to become high? Is it the low calcium? Or what triggers having low ionized calcium, is it the high INTACT PTH?

Several reasons. There are several triggers to high PTH, and you will need to see your doc for workup. Some things that can do this are of primary cause (happens on its own i.e. adenoma), low vitamin D levels, somewhat advanced chronic kidney disease, low calcium levels. As always, labs are just labs, but the clinical context is where the importance lies. Please follow up with your doc about this.