I have exactly this problem as well. I normally run with the Timer set to delete selected data every five minutes. Unfortunately, this Timer state initiates a process called Safari Networking, which takes up 100% to 150% CPU when examined with Activity Monitor. The problem is solved by turning off the Timer function. Unfortunately, I need the Timer function.
This issue reduces my battery operation time (mid-2015 MacBook Pro) from about 6 hours to about 2 hours. I hope Sweet P is working this issue. I'm unable to use the product with Safari, and I'm looking at alternatives.