Data use on streaming on Chromecast topic

A little background here, i am yet to order the google chromecast as i have one question on my mind.
I live in a country where high speed Internet is both expensive and limited. Thus my monthly internet cap is 60 GB for 8Mbps or 1MBps speed.

So my qiestion is , when local content i.e content on my phone , tablet or pc is streamed via wifi to the chromecast , is this data consumed from my internet bandwidth. Say i stream a 2Gb movie , will 2 Gb be deducted from my internet limit as my wifi router was used ?

Sorry if this is a naive question , but I do need some clarification regarding this.

Thanks.