Why did the Dollar weaken after interest rate increase? Yesterday the Fed increased the interest rate of the Dollar yet it's value decreased against various currencies (Source). 

According to this article it should be the other way around :


  In economic theory, if the interest rates in one country increase, then the currency value of that country will increase as a reaction. If the interest rates decrease, then the opposite effect of depreciating currency value will take place.


Source

So why did the value of the Dollar decrease?
It is correct that higher rates should strengthen the dollar... IF


the increase in interest rates is unexpected and
all else equals. 


I haven't followed this particular rate hike, but here is a basic explanations why the dollar might weaken after an increase in interest rates:

The rate hike was widely expected and already priced in by the market, As a result, it didn't have much of an effect on the exchange rate. Keep in mind that the dollar can fluctuate quite significantly even on days without a Fed decision.  The move you refer to might be one of these fluctuations and have nothing to do with the rate hike. Or a small move due to the rate hike might have been overshadowed by a bigger move due to a different factor.

It's worth keeping in mind that it's not the events themselves that matter for exchange rates (or stock prices), but how these events turn out relative to expectations -- markets are forward-looking.