In general, the generic medications work the same as the name brand. They are by definition exactly the same molecular structure. However, they do sometimes have slightly different "fillers" that might result in different levels of absorption. It is possible that this represents the difference between atenolol and Tenormin. In have never had (in my experience) any problems with the generic versions of atenolol. I would say that this situation is probably unique to your situation and I recommend that you discuss this with your cardiologist
If you don't want to pay for the name brand, then you might consider switching to a different beta blocker. Other beta blockers that act similarly to atenolol but might work for you in their generic form. One example is the commonly used metoprolol. This is the medication that I reach for first in some types of SVT.
I suggest that if you are still having issues with your SVT and you cannot get the Tenormin through your current insurance company, then you should schedule an appointment with your cardiologist to discuss this further. Your cardiologist might be able to write your insurance company a letter for a "prior authorization" that might allow it to be covered. If not, then you can come up with an alternative medication that might work just as well.