Context is everything, so let's examine more of the text from your source:
Linda, a 54-year-old event consultant in Los Angeles, is neither disorganised nor innumerate. Ask about her finances, however, and you lose her for two hours. She opens her current (checking) account on a mobile app, then cites a rainy-day fund at another bank. She has 14 credit cards, five mortgages, six insurance policies and several pensions with ex-employers.
The story starts with an anecdote about Linda, who is said to be organized (or at least not "disorganised") and comfortable with numbers (or at least not "innumerate.") But if you ask Linda about her finances, she gets lost in the details of all her accounts, at least thirty by my count. In fact, it will take her two hours to go through everything.
Linda will start talking about her "current (checking) account," which she'll show you by accessing the account on her phone (via a "mobile app"), and then she will reference a fund at another bank, which is called a "rainy-day fund," i.e. a fund for emergencies.
That's what cite means here, to reference as an example. It comes to us from the Latin citare, meaning to call. Notice the contrast between the two bank accounts. The first one, the checking account, Linda will show you using a mobile app; the second one, the emergency-fund account, she won't actually show you. She'll just refer to it.
This is the same usage in a research paper, when the authors cite a source as an example that supports the results in their paper. The source may be a book or another published paper, and it will be called out or referenced by name and other identifying information, but not reproduced in its entirety.
This is the common usage in legal briefs, when lawyers cite precedents, previous court cases that support their legal arguments. These cases will be referenced by title and identifying labels, but their full text will not be copied into the brief.