These websites only say that a homeowner may perform the work, not that a permit is not required. I recommend calling your county/town to inquire. If anything goes wrong and there is damage to the home or property, insurance may deny the claim if there was no permit.
Regarding tandem breakers, the main issue is that many electricians use shared neutral wiring to save on wiring costs. Your house may have shared neutral wiring, or may not, you wouldn't know unless you looked. Shared neutral wiring works fine with regular-sized breakers on opposite-phase hotlines, but is impossible to do if the two circuits are consolidated onto a tandem breaker. This could cause a fire, which, again, would invalidate insurance if they found out that a tandem breaker was the cause. There is a separate issue of certain breaker boxes only rated for tandem breakers in certain slots and not all slots. If any of this sounds new to you, I recommend doing some research and perhaps talk to an electrician to look over the changes you made.