When Han Sen first saw the Nine-Life Cat symbol on Zero, he thought it was just a sign associating her with Blood Legion in some way. Now that Han Sen was thinking about it, he realized the symbol was just like the tattoo on his back.
Zero could enter the sanctuaries without issue, unlike others who were subject to limitations and restrictions. She never had to go through a formal ascension process, either.
Now Han Sen was thinking that if Zero had a Nine-Life Cat symbol like his, the mystery was practically resolved.
Old Cat had said that having Nine-Life Cat blood meant you could come and go in any sanctuary as you pleased. It was a fine explanation for why Zero was able to enter any of the sanctuaries, without ascending the proper way.