It's mentioned in one of the
files (and an
early version). Alex also likens herself to Spencer and Albert as a fellow "
chosen one" and the last left to change the world, and establish a "
new world order".
At the same time, Alex despises Spencer for ruining her life, likely referring to him infecting her in 1998 with a prototype virus that gave her an incurable illness. Neither she or Albert want to particularly "carry out Spencer's wishes", but by succeeding where he failed they'd be superior to him, in their minds.
When Alex speaks of "fear/terror", like infecting the world with it, she's figuratively talking about the world domination plan. She just has another method for artificial selection, making superhumans out of those who can conquer fear, rather than just those who are genetically gifted. Neil also says the tragedy that befell the island would play out
all over the world as well if she succeeded in her mind-copy plan, in other words, Neo Alex would plague the world with a virus, whether t-Phobos or Uroboros. She also refers to herself as "
the Creator", her reincarnation being to obtain a body worthy of that title.
Albert had a disdain for humanity from an early age and always schemed mass extinction and forced evolution before he ever knew Spencer's ultimate goal. His time at Umbrella reinforced it and he sought to use Umbrella and its rival company to take over the world (which may be in-progress) to enact the extinction and evolution he craved. In 2006, the combination of Spencer's plan for Progenitor and the interference of Chris & Jill led him to re-evaluate that perhaps humanity had a chance to redeem itself and become better. That culminated in the Uroboros Project.