An excellent answer (as always, of course) from Chuck.
I'll simply explain the "redirected to a connection that is not secure" bit. That message is usually nothing to worry about. It simply means that you're switching from a secure web page to an 'ordinary' one. For example, you might book some airline tickets online. Throughout the booking process you should be seeing 'https' (and the lock symbol), which means that your debit card details can't go astray. However, when you booking has already been fully completed, there might be a button which says 'Click here to finish'. All that the button does is to take you to an 'ordinary' page, advertising the airline's current special offers. Under those circumstances you might see the message you've referred to but, since you're no longer inputting personal data, there's no cause for concern.
Chris