I have a 98 A4 2.8 with tiptronic and I recently had a similar issue. For me, the front pump to the transmission was bad. At first I thought it was this brass sleeve bearing in the pump housing because it was shot on my original transmission. It showed signs that it ha been spinning and it should not move. I bought a new sleeve bearing and it did not fit right, still leaked tranny fluid. The shot sleeve bearing spun and wore out the housing in the front pump.
I ended up replacing the entire front pump from a car in the wrecking yard. Not fun at all. Have to remove front driveline (if quattro) that goes throught the transmission and I had to unstack the transmission and restack it when putting the thing back together. The job really sucked, but this did fix the issue.
Another option if this happened to you is to have a machine shop make you a sleeve bearing that will fit the worn out pump housing and has proper inside diameter that matches a factory bearing specs. A couple of shops local to me could do this for about $200-250 and that would have been a lot simpler way to go in hindsight.
If it turns out that you nicked the brass sleeve bearing or something while stabbing the tranny, I still have the new one that I purchased and will sell you that cheap. I can also get you more detail if it turns out you need to change the front pump on the transmission.
It is possible that when you put the engine back in, the sleeve bearing I am talking about got stabbed or scratched by the engine side causing it to leak and/or fail.
Let me know if this helps. I also found out that there is a cheaper alternative to that OEM Audi Transmission fluid which tends to be generally very expensive from the dealer. Take a look at buying Redline D4 Automatic transmission fluid. You can get it for around 12 or 13 buck per liter from NAPA (a lot of times by special order only) or as cheap as around ten bucks a liter online but then you have to pay shipping. Consider that it it about $32-36 per liter from Audi dealership and I think the capacity is something close to 6 liters including the torque converter. The redline stuff is synthetic but works fine when mixed with the OEM stuff. Don't put universal $3/quart ATF in your tranny as this is generally not compatible with Audi/VW.
There is a trick to filling the transmission fluid as well. It is a 'sealed' transmission of sorts and does not have a friendly way for end user to fill it up. You need to get it up on jack stands or a lift and remove a 17mm Allen head fill cap towards the back of the tranny. You then need to pick up a hand held fluid pump for about $4 and put the fill hose in the hole after said cap is removed then pump fluid until it overflows out of this hole. Really a lame process but this is the way to get it done. Car should be level.
Consider running car if on jack stands or lift and shift through your gears with tip, then check fluid level again before putting back on ground. This will help to fill up the torque converter if it has lost some fluid during the process. Obviously make sure the wheels are free to spin prior to putting in gear or anything like that.
Let me know if this helps. I just passed 10k miles since I fixed mine a few months ago. You can email me for more on this or if you need that sleeve bearing. Ken ([email protected]) (801) 649-5600

Try inspecting torque converter, (looks like a bundt cake pan) attatched to your flywheel. also did you re-connect your transmission cooler hoses that go to the radiator? hope this helps! oil splashed into your exaust system thereby the smoke.