I don't believe a browser change will help here although I use Firefox. If the e-mail comes in and you click on it, you will be redirected. I got one the other day and observed the address and it definitely not was from ebay which allegedly needed to "update" my credit card information. Be aware, be very aware.
One extension that would be helpful here is the Spoofstick extension. It tells you the real URL of the page you are on.
Phishers are constantly out there.
I get at least three-five ebay or paypal phisher email a week, I believe. I even get some from companies I have no account with. I used to turn them all in. Now I just delete them.
But after awhile, you begin to recognize the scripts, like with the "help the nigerian whatever get money out of the country scam" Someone's with an out of country IP has been using your account. Sometimes you get a message like a very large purchase was made with your account, and you get an oportunity to cancel if you go to this link. Saw a new one last week for paypal...email informing you that a new email address had been added to your account. If you want to verify it, just click here (and they were using an exploit that made it look like the URL was legit). Being an old hand at this, I went directly on another page to PP, and lo and behold, nothing of the kind had happened.
Phishers are evil and should be burned at the stake.