Correct. As per page 9 the most of the budget allocated for the project comes from wikimedia themselves, totaling 2,445,873.00 USD in for the fiscal year 2015-2016.

do these funds come from the donations they solicit on wikipedia.org?

Yes, it's the main (only?) source of income for the Wikimedia Foundation.

There are substantial donations from other foundations and company match programs (Huuuge page):

https://annual.wikimedia.org/2014/#s-5

I guess the foundations aren't reasonably a response to the Jimmy banners, the company matches probably are.