I have an aggressive lovebird rescue...he is biting out of fear but the bite hurts nonetheless ( no...it's not a senegal bite but those little fellas can pack a punch, too.)
What I decided to do first is NOT approach him when he is inside his cage. I think that the cage is their refuge, their safe place, so to speak. If your guy has had an abusive past, it may be unfair and unfortunate, but there is little reason at this point for him to see you or any other human as anything but abusive...and you can't explain that to him. With time, he will come to understand that you are a GOOD person and a LOVING person....right now, he is just scared and angry.
Although my lovebird was fully winged, I found that I could not approach him that way and although I am not a big advocate of clipping, I knew it would be the only way to train him and allow him to see I wouldn't kill him. So, he got clipped. I would only approach him when he came out of the cage and yes, he tried to bite...a lot. But when he flew away and couldn't and flopped ( nice and soft) I was there to "rescue him". He soon learned to climb into my hand...doesn't like the finger...rather likes to be scooped into my hand where he sits snuggly and actually lets me kiss him. Yesterday, for the first time he allowed himself ( after much running around to escape) to be scooped into my hand from the TOP of his cage. A vast improvement.
He still runs inside his happy hut if I put my hand in the cage but I think we have made remarkable progress in 3 months.
So...although I'm not a senegal owner, I can only give you my feeling on the subject. It's hard with a rescue, especially one that has been abused. I never wanted to scold Linus for biting me because he had a bad history and I didn't think that it was fair to do that. I needed to work with him at his pace ( obviously, though, I had to be proactive because his pace would have been NEVER.
)
Turk has been with you a very short time....if he has been abused or mistreated, it will take many months to gain his trust and to boost his confidence. Go very slowly...again, I would try a approach him OUTSIDE the cage rather than INSIDE. If he isn't clipped, I would do so...FOR NOW...so that when he is outside, he won't just fly away from you. Be prepared to be bitten...no fun but it goes with the territory. Try approaching slowly with your hand.....if you see him getting into "launch to attack position"...stop..don't go further. Keep you hand at a comfortable distance from him so he knows you won't hurt him. You can then walk away for a few seconds and try again, approaching slowly and then stopping when he gets anxious. The open hand approach definitely worked better than the finger approach with Linus...I dunno..maybe it'll help with Turk.
Try different things...but don't worry about making things worse. When you aren't an expert in bird rehabilitation, it takes a lot of trial and error to find what works....I'm sure even experts need to modify their approach to accommodate individual birds.
Good luck....and remember. Lots of love and patience will go a long way. I'm sure you will make a great parent to Turk and I'm sure he'll soon realize it.