'As the media focus on Tesco shifts, we have to think about what might [cause] negative coverage,' he said.
In recent months Britain's biggest grocer has had to defend its dominance in the market; commentators have criticised it for creating uniform 'Tescoland' high streets.
Neill said TPF had moved the account out of six-year incumbent Lansons Communications because coverage needed to 'move off the personal finance pages' into more mainstream news.
TPF sells 17 financial products, including insurance, mortgages and credit cards. The group made £200m in 2004 and has around five million customers.
By comparison, Sainsbury's Bank made a £5m loss in the first six months of last year.
TPF typically markets its products through leaflets, targeting Tesco's 15 million weekly shoppers.
But TPF has also marketed National Savings & Investments products since September last year. The pilot scheme to market premium bonds and savings certificates has been extended to more than 700 stores.
QBO Bell Pottinger, Grayling and the Wrigglesworth Consultancy also pitched for the account.