That's inaccurate. There are thousands and thousands of factors which dictate inflation. Yes, there have been some rare cases where prices raised because of minimum wage, but in general, it has been the complete opposite. When you give people more purchasing power, then there is more money flowing throughout the economy and more reason for people to buy goods. Seattle raised their minimum wage to $15 in 2015, and after two years, prices for goods haven't soared because of it.
Also the minimum wage has remained stagnant since the 1970s, and not just minimum wages, but all wages as well. If it were to keep up with inflation, then our minimum wage would be over $12. If it were to keep up based on current productivity, it would be over $20.
Also, if you've watched the video, this doesn't just apply to people in minimum wage jobs. It applies to everyone, including full-time positions.