Men’s fashion has moved out of the realm of the obscure, the twee or dandy. It is the segment of the fashion business that has been steadily ticking upwards in sales. And this week has underscored the reality that there are a host of young menswear brands that have a strong point of view, a wellspring of creative energy and a desire to build real businesses, not just vanity ones.
The sentence might benefit from being reworked slightly. Is men's fashion the only segment that has been experiencing higher sales? If so, perhaps you could try "It is the only segment of the fashion business whose sales have risen in recent years, rather than falling." If not, maybe "It is a segment of the fashion business that whose sales have steadily risen in recent years." You might also try "that has steadily been rising in sales" or "that has steadily been increasing in sales," but both of those sound a little more forced.
"Ticking upwards" almost certainly means an increase, probably occurring in small jumps.
Without much evidence, I suspect that it represents an example of verbing, the conversion of a noun to a verb, and is based on the term "uptick",
uptick: a small increase or rise : "an uptick in sales" "an uptick in hiring" .
I suspect the usage is quite uncommon.