This should NOT be a guess, and it should NOT be a different amount of exposure change based upon the FL of the primary lens or which camera body!
A 2X teleconvertor doubles the FL, without a change to the aperture size (mm), so the effective f/stop of every lens will always be 2 f/stops smaller than without the extender.
Look at the electrical contact pattern of the primary lens, and of the telextender...
- With the 70-200mm lens, a 5 pin + 2(3) pin pattern forms the connections to the body. That matches the 5+2(3) pattern of the 'reporting' telextender, and the body is told about the doubling of the FL as well as the -2EV change to effective aperture. So the body is told [140mm f/5.6 lens - 400mm f/5.6 lens] and it sees a certain quantity of light, Q.
- With the 70-200mm lens, a 5 pin + 2(3) pin pattern forms the connections to the body. That does not match the 5 pin pattern of the 'non-reporting' telextender. So the body is NOT told about the doubling of the FL as well as the -2EV change to effective aperture. So the body is told [70mm f/2.8 lens - 200mm f/2.8 lens] and it sees a certain quantity of light, Q/4. The real truth is [140mm f/5.6 - 400mm f/5.6] lens, and quantity of light Q.
- With another lens (like my Canon 100mm f/2, and maybe your Tamron 90mm), it has only 5 electrical contacts. Regardless of reporting/non-reporting teleconvertor being used, the body is NOT told about the doubling of the FL as well as NOT being told about the -2EV change to effective aperture. The body continues to think [100mm f/2] lens but thinks that quality of light Q/4 (same as -2EV).