I thought the same thing about Czarina. I tried bringing her indoors last December and it was miserable. She was aggressive and incredibly stressed. She peed everywhere and attacked Kiska, who was at the time about 4 months old and recently spayed. I had been keeping Czarina in the hallway area of my apartment and one day she just got out.
She has been an outdoor cat for at least 3 years and she's estimated to be about 3 to 4 years old. I recently took her in again, because it is too dangerous to keep her outside anymore due to a very nasty neighbor who has threatened to poison her.
I spoke to my vet and asked her if there was anything I could give her to at least help her with her stress, anxiety and aggressiveness. My vet spoke with one of her collegues, who suggested prozac. I'm not saying this is the answer to every cat issue, but for me it was. The other vet had used prozac on other patients in the past with the same issues as Czarina, strays also and the results were amazing I was told.
It takes about 3 weeks to begin seeing results, but she will eventually become less anxious and nervous about her new surroundings, which will make it easier to accept the drastic change in her life. She's been on the prozac for 2 weeks tomorrow. I also have a feliway diffuser in the kitchen. She never used to use the litter, and now she is. She's also starting to venture out of her little safe bed and walk around the kitchen now and then. I have her separated from the others by a bamboo screen at the kitchen door opening and a heavy mesh over the pass through. There's a lot of hissing on her part, but not as much as the first time I had her. The first time I had her she was so stressed when she saw the others she foamed at the mouth constantly. Now she doesn't.
Your situation may be different. I don't know how you came by your Tigger. Perhaps bringing them upstairs and keeping them in a safe room together while you work with Tigger may help the situation. She'd not feel so alone with him there with her.