I live on Long Island and I work in Queens. I do about 1,500 miles a month and I am a conservative driver (I get about 270-290 wh per mile on an 85D). The rate on Long Island varies, but over a year it is about 19 cents a kWh. I charge mostly at work and there the rate is about 25 cents. I have solar on my house as well.
I have had my car for over 2 years, and I never heard about them forcing you to switch to TOU (time of use) billing. It is an option and I have read the rate charts. I agree with the post that it usually does not make sense but with solar it makes even less sense. The reason is, with solar, you get a full credit for each kWh produced. If you go to TOU, it divides the production into the 4 possible rates and you cannot use overproduction in one rate for another.
Lastly, my account reconciles in February and I overproduce from the solar. Because of the difference in rate (they give you about 3-4 cents for every kWh overproduced) I will charge the car at home a lot in the winter to use up the overproduction. Even with this, I have not gotten any notice to change to TOU.
To answer the original question, at work, the bill has gone up about $150 a month, so $125 on LI seems reasonable (the rates are about 25% higher in Queens).