...Should a publisher ask me for money?


NO! Legitimate publishing houses never charge the author, they will pay for everything. This is why publishers take a cut of an author's royalties. They make an agreement that they will produce, print, and distribute your book in exchange for a percentage of royalties. 

If a 'publisher' is asking you to foot the bill for all the expenses attached to publishing, they are vanity presses. While the businesses are not illegal, they are considered ethically immoral amongst the community. Money should always flow to the author in traditional publishing. If you are ever contacted by a vanity press, don’t engage.