@Michel If you haven’t done it recently, it may be worthwhile to do a DIA test and a carb absorption rate test. When I did this a few months ago I was astonished that novolog had an almost eight hour tail for me. The fact that this problem is contiguous with starting the pump could point to novolog as the basal insulin being at fault.
When the insulin regimen was Regular and NPH, this was the cause of most problems. The graphs that these calculations will produce can be very revealing.