The science behind it is that red light promotes flowering. This is seen in growth and flowering differences when using metal halide grow lights (low in red) vs. high pressure sodium lights (high in red light). But it is questionable as to the practical effectiveness of inducing this effect outside.
Its been a while since I read one of the university studies, but as I recall it found a slight statistically significant increase in fruit number (?10-15%) with red plastic ground cover under certain conditions but there was a lot of variability. A large commercial outfit might be able to get an increase in profit, but with a few plants a home gardener probably couldn't get consistent results based on the numbers I saw. The major down side was that the experimental trial that showed a difference from the control required quite a bit of space between plants so that enough light could hit the plastic and reflect back up to the plants. You would get more production by simply fitting more plants in the same amount of space (normal spacing). The study was to see if it could work, it was not a study to look at practical application.
Of course the people who make over-priced do-dads for growing tomatoes take those slim results out of context and tell the public that their 1sq ft plant doily that fits around the base of the plant will do miracles.