It would be naive to believe that she made the exit completely willingly and on her own terms.
DBS could not have sacked her outright for insubordination or "conduct unbecoming of a leader". Certainly not right after the AWARE saga. Christians everywhere, and not just the fundies, would have been up in arms. That would have been layering disaster atop disaster. There would have been another boycott of DBS's products and services, this time by the larger and more ungulate-like of the Christian Singaporean demographic.
So. What probably happened was that she must have been sidelined for a considerable length of time in DBS, while still nominally remaining Head of Marketing. It would have been the politic move to make for the powers that be in DBS. Now that several months have passed and the fires have died down, they must have made it clear to her in no uncertain terms to "please leave".
The funny thing here is that, as the article makes clear, Josie Lau has been hired by OUE through personal connections. After all, what are feminist mentos for? Not just for freshmaking or coke eruptions, apparently.
Seriously though, it's unlikely she will ever be hired by another large company in Singapore again, other than through personal connections. Her resume is now, how shall we put it, radioactive.
Another funny tidbit. As one of the commentors in the news article pointed out, a fair number of the tenants in Mandarin Gallery are gay friendly, which isn't exactly a surprise since the fashion industry is stuffed to the rafters with people who swing that way. That might make any working relationship between Mizz Lau and her tenants ... difficult.
So as for our dear Josie looking forward to working in fashion, well, she might love fashion, but I doubt fashion loves her, dahling.