This is pretty standardized in many US-based software jobs - the employer gives you an Assignment of Inventions bit of paper in which you agree they own a chunk of your brain, you add additional bits of paper where you and the employer agree to exclude specific things, say, your personal open-source groupon for kittens. It's usually routine and painless.
It should be noted that many states, including CA puts limits on what can be covered by this language.
Under California law, an employee cannot be required to assign any of his or her rights in an invention he or she develops “entirely on his or her own time without using the employer’s equipment, supplies, facilities, or trade secret information”
There are exceptions, see the whole article. This case even if in CA may be marred by the "Trade Secrets" restriction.
The next line from your clip seems really relevant to this topic
when the invention was conceived or “reduced to practice” (actually created or a patent application filed) it related to the employer’s business or actual or “demonstrably anticipated” research or development, or...
In other words, if it's related to the employer's business it belongs to them. What's related and what is not is up to a judge to decide. There's arguably a spectrum of directly related, somewhat related, tangentially related, unrelated, etc.. Seems like the OP's project though is in the directly related side of the spectrum.
One of those exceptions is potentially rather significant here, though. From immediately after the part you quoted:
unless:
when the invention was conceived or “reduced to practice” (actually created or a patent application filed) it related to the employer’s business or actual or “demonstrably anticipated” research or development,
That said, the article you linked to seems to be about patents covering inventions rather than copyright covering creative works, so without reading more about the laws in those states I don't know whether any of this is actually relevant in this case.
