Confused about the wording may be different states. You say your license you have 0 but MVR is 13. When you say license to you mean your insurance points? I think your drivers license is issued thru the DMV same place that you pull MVR from.
Yes certainly MVR points often vary to insurance points. They don't use the same rating. Also the insurance company doesn't always pull the MVR report at renewal. They do it randomly because it would be expensive to pull every single insured person. Depends on the company and what sort of risk they want to assume.
In my case when I had my DUI the insurance company only knew because there was a property claim because I was involved in an accident. They did NOT drop me and I don't recall a large increase in my premium (25 years ago).