I have never worked with Tambotie, it is pretty. If it is oily, then I would also highly suggest wiping down with acetone or DNA before applying CA. I have found that I need to do this with many exotic woods such as African Blackwood, Bloodwood, Cocobola and others, to prevent the exact problems your describing.
When I'm ready to apply the finish I will use a clean piece of shop towel with some acetone. I will clean it a few times until there is very little color coming off the blank. Let it sit for a minute, to ensure all the acetone is evaporated, then I apply CA as normal. Two coats of thin, to soak in,then about six coats of med. I use a quick spritz of accelerator and 30-60 second wait between each coat. I have not had a lifted or cracked finish since I started this.
I figure the acetone is drawing out sufficient oil to let the CA fully cure before the oil leeches back to the surface. Once the CA is well cured, then all is well. This is why you need to apply the CA right after the acetone. If you leave it for a day, or even a couple of hours sometimes, your right back where you started.
I personally don't use BLO because I found it sometimes caused similar problems.
Hope you get this working.