The white fluid was probably her's- that is often the color of women's secretions or the mix of body fluids... that could be just the base of your penis 'sweating' and mixing with her fluids. The fact, however, that you had semen in the shaft of the condom is not so great- a tighter fit should have kept all the semen at the tip of the condom. It does sound like there could have been some leakage.
If I were you , I would have her make sure that no pregnancy resulted. The chances are always small that a small amount of seminal fluid will impregnate a woman - you need multiple millions of sperm to get one of them to hit an egg and fertilize it. Nonetheless, stranger things have happened-and this deserves a quick visit to her gynecologist to see if she is ok or not. Assuming she is, make sure to look over condom brands in the future to make sure you get one with a tight fit. Also buy standard brands that have a valid date on them that shows they are still effective. Put the condom on very carefully , making sure that it is tight at the bottom and that you have not snagged it with a nail or hurt it when tearing open the package. Standard brands like Trojan or Durex have very low failure rates-- but it is possible to put them on incorrectly. Also, if you have been making love a long time and done a lot of thrusting, you might want to put on a new one- just to be safer.
Condoms are a great contraceptive method- but take care to do it right. And do find out right away if that semen escaped enough to cause an accidental pregnancy.
Thanks. Some followup questions.
Is there a way to check if she got pregnant immediately? Just to avoid having her take the "next day pill" unnecessarily..
She is supposed to have her period in the next couple of days, That would mean she is at her unfertile stage, right?
There is no way to know if she is pregnant now. You would have to wait at least 2 weeks. But since her period is due in a few days she has probably already ovulated and you should be fine. But she could get the morning after pill just in case, but I think your in the clear.