Weld-o-let is a trade name, so you will not find the welding requirements in any of the ASME pressure piping codes. You need to look up the welding requirements under the heading of: Integrally reinforced branch fittings.
In general, the fitting is welded with a CJP groove weld with a reinforcing fillet weld. The CJP groove weld is flush to the edge of the first bevel if there is a compound bevel. The size of the reinforcing fillet is dependent on the specific pressure piping code specified by the Owner.
As far as the problem with the run pipe becoming oval and excessively distorted, the fewer weld passes to achieve the required weld size the better. Distortion is related to the number of weld beads. The more weld beads, the greater the distortion. You could try pre-cambering the run pipe before cutting the hole for the integrally reinforced branch fitting.
The branch fitting should be hand contoured by grinding to ensure a uniform root opening all around the branch fitting before tacking it into position. Most of the fittings are sized by the manufacturer to fit a range of run pipe diameters if the contractor takes the time needed to properly contour the fitting before welding it to the run pipe. Some contractors do not take the step of properly hand fit the branch fitting and then they complain when they don't achieve the required CJP groove weld.
Several fitting manufacturers have websites that address the need to properly fit the fitting and how to weld them to meet code requirements.
Best regards - Al