Does a star's mass determine when fusion reactions start?
Nuclear fusion starts when the star's core temperature is greater than 4,000,000K and it is not directly dependent on mass.
Stars are formed by clouds of gasses forming regions which collapse under gravity. This process can take millions of years. Material more gasses keep falling into the protostar increasing mass.
In-falling gasses make the core of the protostar start to heat up. It is only when the core reaches a temperature of more than 4,000,000K that Hydrogen fusion can start,
Main sequence stars have to be in hydrostatic equilibrium. This occurs when gravity, which is trying to collapse the star, is balance out by outward pressure from fusion reactions.
Once fusion is taking place, the solar winds prevent further material increasing the mass of the star.
So, the final mass of a star is determined by its mass when the core temperature it hot enough to start fusion. This required a mass of at least 8% of that of the Sun.
Very massive stars are quite rare as fusion tends to start at lower masses.