First off the spray was probably Boomer's anal glands. Just like dogs, cats can release them when they are scared.
I'm guessing Ginger just thought potential playmate when she sprang off the couch after him.
When we adopted Ramone he showed way too much interest in the cats, and not in a good way. For awhile I wasn't sure we'd be able to make it work, as I wasn't willing to live in a segregated house (ie. dogs upstairs, cats downstairs).
What we did is we took Flea and put him in his carrier. Then we put Ramone on a leash and led him by the carrier to sniff Flea. Flea felt safe and we had control of Ramone. I made him sit by the crate and I clicked and treated him every time he looked away from it. It took awhile at first because he wanted Flea really badly.
When he learned that he got treats for looking away from Flea I opened the door of the carrier. Flea came out and started sniffing around. This excited Ramone at first, but because we had him on leash he couldn't charge Flea. I had him in a down at this time because dogs aren't as likely to break a down as they are a sit. Again I clicked and treated every time he looked away from Flea.
It took a couple sessions, but now they are good friends. Well they are more like siblings. Sometimes they love each other and other times they torment each other.
I also think that it is good that you have a safe room where Boomer can go that Ginger can't get into. I think that is very important.
As for letting Boomer teach Ginger a lesson... it can work very nicely... or it can end up expensive if Boomer gets her in the eye. Also if Boomer is the type of cat that runs first and asks questions later she will only learn that chasing cats is fun. In that case you have to make sure you teach the lesson that chasing cats isn't fun.
I hope you can take something from my experience with Ramone and my cats to help you. Good luck!