Generally, an Ontario driver convicted of a driving offense in the State of New York  will acquire points just as if the offense happened in Ontario. 

The specific convictions from New York that will add demerit points are:  

• speeding
• failure to obey a stop sign
• failure to obey a signal light
• failure to stop for a school bus
• racing
• failing to remain at or return to the scene of an collision
• careless driving

See: https://www.ontario.ca/page/understanding-demerit-points#section-6

Based on the information from the Ontario Ministry of Transportation, it appears that a conviction for unsafe lane change or following too closely would add points to an Ontario driving record.* 

This is good news for the driver but demerit points are not the only consideration. Pleading guilty to these tickets would incur total fines from the court of up to $300 plus a $186 surcharge. And the New York Driver Responsibility Assessment would cost the driver $375. Additionally, the driver's insurance company may raise premiums or even drop coverage. 

Never plead guilty to any ticket without first fully understanding the consequences and options. Always call a lawyer first, we offer free consultations, you might as well take advantage. 

*We are not licensed to practice law in Ontario and this is not legal advice. For a definitive interpretation please consult a Canadian lawyer.